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laurentMatrix

Create Laurent matrix

    Description

    Use the laurentMatrix object to create a matrix with laurentPolynomial elements. You can perform mathematical operations on the matrices.

    Creation

    Description

    lmat = laurentMatrix creates a Laurent matrix that is a 2-by-2 identity matrix.

    example

    lmat = laurentMatrix(Elements=entries) creates a Laurent matrix with elements specified by the value of the Elements property.

    Properties

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    Laurent matrix elements, specified as a cell array that has at most two rows and two columns. You can specify an element as a real-valued scalar or laurentPolynomial object. laurentMatrix converts all real-valued scalars into laurentPolynomial objects internally.

    Example: lmat = laurentMatrix(Elements={2,4;lpA,lpB}) creates a 2-by-2 Laurent matrix, where lpA and lpB are both laurentPolynomial objects.

    Object Functions

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    ctransposeLaurent matrix transpose
    detLaurent matrix determinant
    dispMatDisplay Laurent matrix
    inverseLaurent matrix inverse
    dyaddownDyadic downsampling of Laurent polynomial or Laurent matrix
    dyadupDyadic upsampling of Laurent polynomial or Laurent matrix
    eqLaurent polynomials or Laurent matrices equality test
    plusLaurent polynomial or Laurent matrix addition
    minusLaurent polynomial or Laurent matrix subtraction
    mtimesLaurent polynomial or Laurent matrix multiplication
    reflectLaurent polynomial or Laurent matrix reflection
    uminusUnary minus for Laurent polynomial or Laurent matrix

    Examples

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    Create two Laurent polynomials:

    • a(z)=2+4z-1+6z-2

    • b(z)=z2+3z+5

    lpA = laurentPolynomial(Coefficients=[2 4 6]);
    lpB = laurentPolynomial(Coefficients=[1 3 5],MaxOrder=2);

    Create the Laurent matrix [-1a(z)b(z)7].

    lmat = laurentMatrix(Elements={-1 lpA; lpB 7});

    Display the elements of the matrix.

    for j=1:2
        for k=1:2
            fprintf("===================\nlmat(%d,%d):\n",j,k);
            element = lmat.Elements{j,k}
        end
    end
    ===================
    lmat(1,1):
    
    element = 
      laurentPolynomial with properties:
    
        Coefficients: -1
            MaxOrder: 0
    
    
    ===================
    lmat(1,2):
    
    element = 
      laurentPolynomial with properties:
    
        Coefficients: [2 4 6]
            MaxOrder: 0
    
    
    ===================
    lmat(2,1):
    
    element = 
      laurentPolynomial with properties:
    
        Coefficients: [1 3 5]
            MaxOrder: 2
    
    
    ===================
    lmat(2,2):
    
    element = 
      laurentPolynomial with properties:
    
        Coefficients: 7
            MaxOrder: 0
    
    

    Extended Capabilities

    Introduced in R2021b