inverse

Laurent matrix inverse

Since R2021b

Syntax

R = inverse(M)

Description

R = inverse(M) returns the inverse of the Laurent matrix M if M has a nonzero monomial determinant.

Examples

Laurent Matrix Inverse

Create the Laurent polynomials:

• $$a(z)=z+1$$

• $$b(z)=z^2+z+z^{-1}$$

• $$c(z)=z$$

• $$d(z)=z^2+z^{-1}$$

lpA = laurentPolynomial(Coefficients=[1 1],MaxOrder=1);
lpB = laurentPolynomial(Coefficients=[1 1 0 1],MaxOrder=2);
lpC = laurentPolynomial(Coefficients=[1],MaxOrder=1);
lpD = laurentPolynomial(Coefficients=[1 0 0 1],MaxOrder=2);

Create the matrix lmat = $\left[\begin{array}{cc}\mathit{a}\left(\mathit{z}\right)& \mathit{b}\left(\mathit{z}\right)\\ \mathit{c}\left(\mathit{z}\right)& \mathit{d}\left(\mathit{z}\right)\end{array}\right]$. Obtain the determinant of lmat.

lmat = laurentMatrix(Elements={lpA,lpB;lpC,lpD});
det(lmat)

ans = 
  laurentPolynomial with properties:

    Coefficients: 1
        MaxOrder: -1

The determinant is a nonzero monomial. Obtain the inverse of lmat. Inspect the elements of the inverse.

lmatinv = inverse(lmat);
lmatinv.Elements{1,1}

ans = 
  laurentPolynomial with properties:

    Coefficients: [1 0 0 1]
        MaxOrder: 3

lmatinv.Elements{1,2}

ans = 
  laurentPolynomial with properties:

    Coefficients: [-1 -1 0 -1]
        MaxOrder: 3

lmatinv.Elements{2,1}

ans = 
  laurentPolynomial with properties:

    Coefficients: -1
        MaxOrder: 2

lmatinv.Elements{2,2}

ans = 
  laurentPolynomial with properties:

    Coefficients: [1 1]
        MaxOrder: 2

Confirm the product of lmat and its inverse is equal to the identity matrix.

matprod = lmat*lmatinv;
matprod.Elements{1,1}

ans = 
  laurentPolynomial with properties:

    Coefficients: 1
        MaxOrder: 0

matprod.Elements{1,2}

ans = 
  laurentPolynomial with properties:

    Coefficients: 0
        MaxOrder: 0

matprod.Elements{2,1}

ans = 
  laurentPolynomial with properties:

    Coefficients: 0
        MaxOrder: 0

matprod.Elements{2,2}

ans = 
  laurentPolynomial with properties:

    Coefficients: 1
        MaxOrder: 0

Input Arguments

M — Laurent matrix

laurentMatrix object

Laurent matrix, specified as a laurentMatrix object.

Output Arguments

R — Inverse

laurentMatrix object

Inverse of a Laurent matrix, returned as a laurentMatrix object.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2021b