WOLFRAM

Wolfram Language & System Documentation Center
Wolfram Language Home Page »

SymmetricMatrixQ
✖
SymmetricMatrixQ

✖

gives True if m is explicitly symmetric, and False otherwise.

Details and Options

  • A matrix m is symmetric if m==Transpose[m].
  • SymmetricMatrixQ works for symbolic as well as numerical matrices.
  • The following options can be given:
  • SameTest Automaticfunction to test equality of expressions
    Tolerance Automatictolerance for approximate numbers
  • For exact and symbolic matrices, the option SameTest->f indicates that two entries mij and mkl are taken to be equal if f[mij,mkl] gives True.
  • For approximate matrices, the option Tolerance->t can be used to indicate that all entries Abs[mij]≤t are taken to be zero.
  • For matrix entries Abs[mij]>t, equality comparison is done except for the last bits, where is $MachineEpsilon for MachinePrecision matrices and for matrices of Precision .

Examples

open allclose all

Basic Examples  (2)Summary of the most common use cases

Test if a 2×2 numeric matrix is explicitly symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-hvfpa4
Out[1]=1

Test if a 3×3 symbolic matrix is explicitly symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-cssqjo
Out[1]=1

Scope  (10)Survey of the scope of standard use cases

Basic Uses  (6)

Test if a real machine-precision matrix is symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-c1lz7v
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-u5nvc8
Out[2]=2

A real symmetric matrix is also Hermitian:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-be7x8u
Out[3]=3

Test if a complex matrix is symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-vd1q50
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-evd1wm
Out[2]=2

A complex symmetric matrix has symmetric real and imaginary parts:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-cfj13l
Out[3]=3

Test if an exact matrix is symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-fhbhm1
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-joxfpi
Out[2]=2

Make the matrix symmetric:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-cnbo4m
Out[3]=3

Use SymmetricMatrixQ with an arbitrary-precision matrix:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-h89ze5
Out[1]=1

A random matrix is typically not symmetric:

In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-e792ql
Out[2]=2

Use SymmetricMatrixQ with a symbolic matrix:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-p54id
Out[1]=1

The matrix becomes symmetric when :

In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-fz0wna
Out[2]=2

SymmetricMatrixQ works efficiently with large numerical matrices:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-bjhh1d
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-n2hz99
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-pcc5uf
Out[3]=3

Special Matrices  (4)

Use SymmetricMatrixQ with sparse matrices:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-g2yb2
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-dkghyq
Out[2]=2

Use SymmetricMatrixQ with structured matrices:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-f39gxg
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-c0k3bb
Out[2]=2

Use with a QuantityArray structured matrix:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-so3bn
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-d4v8l
Out[4]=4

The identity matrix is symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-kkhgb9
Out[1]=1

HilbertMatrix is symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-ou7ra
Out[1]=1

Options  (2)Common values & functionality for each option

SameTest  (1)

This matrix is symmetric for a positive real , but SymmetricMatrixQ gives False:

In[18]:=18
✖
https://wolfram.com/xid/0d6dlp3lb3-em2aht
In[19]:=19
✖
https://wolfram.com/xid/0d6dlp3lb3-ej0bsf
Out[19]=19

Use the option SameTest to get the correct answer:

In[20]:=20
✖
https://wolfram.com/xid/0d6dlp3lb3-63zf1y
Out[20]=20

Tolerance  (1)

Generate a real-valued symmetric matrix with some random perturbation of order 10-14:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-shf270
In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-bevb8i
Out[4]=4

Adjust the option Tolerance to accept this matrix as symmetric:

In[5]:=5
✖
https://wolfram.com/xid/0d6dlp3lb3-5fapn2
Out[5]=5

The norm of the difference between the matrix and its transpose:

In[6]:=6
✖
https://wolfram.com/xid/0d6dlp3lb3-cd27uf
Out[6]=6

Applications  (13)Sample problems that can be solved with this function

Generating Symmetric Matrices  (4)

Any matrix generated from a symmetric function is symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-dvanq2

The function is symmetric:

In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-fr35le
Out[2]=2

Using Table generates a symmetric matrix:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-e73hcz
Out[3]=3

SymmetrizedArray can generate matrices (and general arrays) with symmetries:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-qyltj4
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-bxfo4l
Out[2]=2

Convert back to an ordinary matrix using Normal:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-x4r0b3
Out[3]=3

Check that matrices drawn from GaussianOrthogonalMatrixDistribution are symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-b8i9rt
Out[1]=1

Matrices drawn from CircularOrthogonalMatrixDistribution are symmetric and unitary:

In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-evoccp
Out[2]=2

Every Jordan matrix is similar to a symmetric matrix. Since any square matrix is similar to its Jordan form, this means that any square matrix is similar to a symmetric matrix. Define a function for generating an Jordan block for eigenvalue :

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-emcq7d

For example, here is the Jordan matrix of dimension 4 for the eigenvalue :

In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-vf9x6g

Define a function for generating a corresponding complex similarity transformation:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-1hkfxf

The matrix is a sum of times the identity matrix and times the backward identity matrix:

In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-gj4alh

Then s(n).j(lambda,n).TemplateBox[{{s, (, n, )}}, Inverse] is symmetric, which shows that the Jordan matrix is similar to a symmetric matrix:

In[5]:=5
✖
https://wolfram.com/xid/0d6dlp3lb3-w5xfly

Confirm the matrix is symmetric:

In[6]:=6
✖
https://wolfram.com/xid/0d6dlp3lb3-w1x2cg
Out[6]=6

Examples of Symmetric Matrices  (5)

The Hessian matrix of a function is symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-kskfqk
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-hu2rz2
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-osa25t
Out[3]=3

Many special matrices are symmetric, including FourierMatrix:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-ji4i66
Out[1]=1

HadamardMatrix:

In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-ltzqa5
Out[2]=2

HankelMatrix:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-b0kry5
Out[3]=3

And HilbertMatrix:

In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-bgcub
Out[4]=4

Visualize the matrix types:

In[5]:=5
✖
https://wolfram.com/xid/0d6dlp3lb3-d6bzd3
Out[5]=5

Many filter kernel matrices are symmetric, including DiskMatrix:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-e3crdl
Out[1]=1

CrossMatrix:

In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-hhv3t
Out[2]=2

DiamondMatrix:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-ekwb7g
Out[3]=3

Visualize the matrices:

In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-n0owqi
Out[4]=4

AdjacencyMatrix of an undirected graph is symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-bv0dcf
Out[1]=1
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-x5yw5r
Out[2]=2

As is KirchhoffMatrix:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-mozazl
Out[3]=3
In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-ztsm28
Out[4]=4

Visualize adjacency and Kirchhoff matrices for different graphs:

In[5]:=5
✖
https://wolfram.com/xid/0d6dlp3lb3-0izfi
Out[5]=5

Several statistical measures are symmetric matrices, including Covariance:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-g93hx1
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-bgvzb5
Out[2]=2

Correlation:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-wzxzm
Out[3]=3

AbsoluteCorrelation:

In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-grp31s
Out[4]=4

Uses of Symmetric Matrices  (4)

A positive-definite, real symmetric matrix or metric defines an inner product by :

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-xs2xkr
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-i29f9p

Verify that is in fact symmetric and positive definite:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-hlh693
Out[3]=3

Orthogonalize the standard basis of TemplateBox[{}, Reals]^n to find an orthonormal basis:

In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-9jtyba
Out[4]=4

Confirm that this basis is orthonormal with respect to the inner product :

In[5]:=5
✖
https://wolfram.com/xid/0d6dlp3lb3-mkuz95
Out[5]=5

The moment of inertia tensor is the equivalent of mass for rotational motion. For example, kinetic energy is , with taking the place of the mass and angular velocity taking the place of linear velocity in the formula . can be represented by a positive-definite symmetric matrix. Compute the moment of inertia for a tetrahedron with endpoints at the origin and positive coordinate axes:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-v3vcks

Verify that the matrix is symmetric:

In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-flo6z5
Out[2]=2

Compute the kinetic energy if its angular velocity is :

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-roafy1
Out[3]=3

The kinetic energy is positive as long as is nonzero, showing the matrix was positive definite:

In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-oesjhx
Out[4]=4

Determine if a sparse matrix is structurally symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-thiqo
Out[1]=1

The matrix is not symmetric:

In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-di0ziq
Out[2]=2

But it is structurally symmetric:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-ntplyc
Out[3]=3

Use a different method for symmetric matrices, with failover to a general method:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-cwrw3t

Construct real-valued matrices for testing:

In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-bzxact

For a non-symmetric matrix m, the function myLS just uses Gaussian elimination:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-nrymt
Out[3]=3

For a symmetric indefinite matrix ms, try Cholesky and continue with Gaussian elimination:

In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-jlyoju
In[5]:=5
✖
https://wolfram.com/xid/0d6dlp3lb3-n81f4
Out[5]=5

For a symmetric positive-definite matrix mpd, try Cholesky, which succeeds:

In[6]:=6
✖
https://wolfram.com/xid/0d6dlp3lb3-b8l0ms
In[7]:=7
✖
https://wolfram.com/xid/0d6dlp3lb3-4l38u9
Out[7]=7
In[8]:=8
✖
https://wolfram.com/xid/0d6dlp3lb3-bvwz55
Out[8]=8

Properties & Relations  (14)Properties of the function, and connections to other functions

SymmetricMatrixQ[x] trivially returns False for any x that is not a matrix:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-dqapjm
Out[1]=1

A matrix is symmetric if mTranspose[m]:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-1hq6q
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-l6roya
Out[2]=2

A real-valued symmetric matrix is Hermitian:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-c69qw1
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-lhf692
Out[2]=2

But a complex-valued symmetric matrix may not be:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-in0t7b
In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-mwta3y
Out[4]=4

Use Symmetrize to compute the symmetric part of a matrix:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-brvqok
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-6nfuuv
Out[2]=2

This equals the average of m and Transpose[m]:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-7p8qam
Out[3]=3

Any matrix can be represented as the sum of its symmetric and antisymmetric parts:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-btttfc
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-ioxqc
Out[2]=2

Use AntisymmetricMatrixQ to test whether a matrix is antisymmetric:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-otom5j
Out[3]=3

If is a symmetric matrix with real entries, then is antihermitian:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-5guo83
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-hqo6rz
Out[2]=2

MatrixExp[I m] for real symmetric m is unitary:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-m8xru
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-bcyqur
Out[2]=2

A real-valued symmetric matrix is always a normal matrix:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-ibz4t6
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-bmf0bo
Out[2]=2

A complex-valued symmetric matrix need not be normal:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-qz67pn
In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-eb23tl
Out[4]=4

Real-valued symmetric matrices have all real eigenvalues:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-emyf98
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-gqjpoz
Out[2]=2

Use Eigenvalues to find eigenvalues:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-bx6amt
Out[3]=3

Note that a complex-valued symmetric matrix may have both real and complex eigenvalues:

In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-zm6f3b
Out[4]=4

CharacteristicPolynomial[m,x] for real symmetric m can be factored into linear terms:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-uetwl5
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-2ncihd
Out[2]=2

Real-valued symmetric matrices have a complete set of eigenvectors:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-gas7tm
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-fetnrq
Out[2]=2

As a consequence, they must be diagonalizable:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-74hwjf
Out[3]=3

Use Eigenvectors to find eigenvectors:

In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-edsq1a

Note that a complex-valued symmetric matrix need not have these properties:

In[5]:=5
✖
https://wolfram.com/xid/0d6dlp3lb3-1nzk4l
In[6]:=6
✖
https://wolfram.com/xid/0d6dlp3lb3-rl3j4s
Out[6]=6

The inverse of a symmetric matrix is symmetric:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-n8jjxz
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-r8bkoa
Out[2]=2

Matrix functions of symmetric matrices are symmetric, including MatrixPower:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-x6n7b
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-n1hh3t
Out[2]=2

MatrixExp:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-0cu58
Out[3]=3

And any univariate function representable using MatrixFunction:

In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-b794x3
Out[4]=4

SymmetricMatrix can be used to explicitly construct symmetric matrices:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-cr5xbx
Out[1]=1

These satisfy SymmetricMatrixQ:

In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-o0d3a
Out[2]=2

Possible Issues  (1)Common pitfalls and unexpected behavior

SymmetricMatrixQ uses the definition TemplateBox[{m}, Transpose]=m for both real- and complex-valued matrices:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-dvg8va
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-jnorqo
Out[2]=2

These complex matrices need not be normal or possess many properties of self-adjoint (real symmetric) matrices:

In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-j4rs3c
Out[3]=3

HermitianMatrixQ tests the condition TemplateBox[{m}, ConjugateTranspose]=m for self-adjoint matrices:

In[4]:=4
✖
https://wolfram.com/xid/0d6dlp3lb3-xdwwzp
Out[4]=4

Alternatively, test if the entries are real to restrict to real symmetric matrices:

In[5]:=5
✖
https://wolfram.com/xid/0d6dlp3lb3-nql4v5
In[6]:=6
✖
https://wolfram.com/xid/0d6dlp3lb3-vgzldd
Out[6]=6

Neat Examples  (1)Surprising or curious use cases

Images of symmetric matrices including FourierMatrix:

In[1]:=1
✖
https://wolfram.com/xid/0d6dlp3lb3-ej1zt
In[2]:=2
✖
https://wolfram.com/xid/0d6dlp3lb3-e4anw5
Out[2]=2
In[3]:=3
✖
https://wolfram.com/xid/0d6dlp3lb3-cjr8o5
Out[3]=3
Wolfram Research (2008), SymmetricMatrixQ, Wolfram Language function, https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html (updated 2014).
✖
Wolfram Research (2008), SymmetricMatrixQ, Wolfram Language function, https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html (updated 2014).

Text

Wolfram Research (2008), SymmetricMatrixQ, Wolfram Language function, https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html (updated 2014).

✖
Wolfram Research (2008), SymmetricMatrixQ, Wolfram Language function, https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html (updated 2014).

CMS

Wolfram Language. 2008. "SymmetricMatrixQ." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html.

✖
Wolfram Language. 2008. "SymmetricMatrixQ." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html.

APA

Wolfram Language. (2008). SymmetricMatrixQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html

✖
Wolfram Language. (2008). SymmetricMatrixQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html

BibTeX

@misc{reference.wolfram_2025_symmetricmatrixq, author="Wolfram Research", title="{SymmetricMatrixQ}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html}", note=[Accessed: 10-July-2025 ]}

✖
@misc{reference.wolfram_2025_symmetricmatrixq, author="Wolfram Research", title="{SymmetricMatrixQ}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html}", note=[Accessed: 10-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_symmetricmatrixq, organization={Wolfram Research}, title={SymmetricMatrixQ}, year={2014}, url={https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html}, note=[Accessed: 10-July-2025 ]}

✖
@online{reference.wolfram_2025_symmetricmatrixq, organization={Wolfram Research}, title={SymmetricMatrixQ}, year={2014}, url={https://reference.wolfram.com/language/ref/SymmetricMatrixQ.html}, note=[Accessed: 10-July-2025 ]}