Construct a Cauchy matrix:

Show the elements:

Normal can convert a CauchyMatrix to its ordinary representation:

Construct a Cauchy matrix with symbolic entries:

Show the elements:

Get the determinant:

Generate a symmetric Cauchy matrix:

Show the elements:

Get the normal representation:

Generate a rectangular Cauchy matrix:

Show the elements:

Get the normal representation:

Represent a dense Cauchy matrix as a structured array:

Show the elements:

The structured representation typically uses much less memory:

CauchyMatrix objects include properties that give information about the array:

The "XVector" and "YVector" properties give the generating vectors of the Cauchy matrix:

The "Summary" property gives a brief summary of information about the array:

The "StructuredAlgorithms" property lists the functions that have structured algorithms:

When appropriate, structured algorithms return another CauchyMatrix object:

The transpose is also a CauchyMatrix:

The product of a Cauchy matrix and its transpose is no longer a Cauchy matrix:

Represent the Hilbert matrix as a CauchyMatrix:

Compare with HilbertMatrix:

Numerically compute the inverse for a large Hilbert matrix:

The result from the structured version is more accurate:

Use CauchyMatrix to compute the coefficients for an interpolating rational function with fixed poles:

Construct the rational function:

Visualize the interpolant in the complex plane:

Check that the rational interpolant does pass through all the given points:

Define the Parter matrix as a CauchyMatrix:

The Parter matrix is both a Cauchy matrix and a Toeplitz matrix:

The Parter matrix's dominant singular values are clustered around :

Express a Cauchy matrix as a product of diagonal matrices, Vandermonde matrices and their inverses:

Express a Cauchy matrix as a product of diagonal, Vandermonde and Hankel matrices: