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inverse

Laurent matrix inverse

    Description

    example

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

    Examples

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    Create the Laurent polynomials:

    • a(z)=z+1

    • b(z)=z2+z+z-1

    • c(z)=z

    • d(z)=z2+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 = [a(z)b(z)c(z)d(z)]. 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

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    Laurent matrix, specified as a laurentMatrix object.

    Output Arguments

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    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

    See Also

    Functions

    Objects