Matrix

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NAME

Matrix - Matrix of Reals

Implements overrides for MatrixReal.pm for WeBWorK In general it is better to use MathObjects Matrices (Value::Matrix) in writing PG problem. The answer checking is much superior with better error messages for syntax errors in student entries. Some of the subroutines in this file are still used behind the scenes by Value::Matrix to perform calculations, such as decompose_LR().

DESCRIPTION

SYNOPSIS

Matrix Methods:

        Method $matrix->_stringify() 
        -- overrides MatrixReal1 display mode

Accessor functions

        (these are deprecated for direct use.  Use the covering Methods
         provided by MathObject Matrices instead.)
         
        L($matrix) - return matrix L of the LR decomposition
        R($matrix) - return matrix R of the LR decomposition
        PL($matrix) - return permutation matrix
        PR($matrix) - return permutation matrix
        Original matrix is  PL * L * R *PR = M 
        

Obtain the Left Right matrices of the decomposition and the two pivot permutation matrices the original is M = PL*L*R*PR

        Method $matrix->rh_options

Meant for internal use when dealing with MatrixReal1

        Method $matrix->trace
        
        Returns: scalar which is the trace of the matrix.
        
        Used by MathObject Matrices for calculating the trace. 
        Deprecated for direct use in PG questions.
        Method    $new_matrix = $matrix->new_from_array_ref ([[a,b,c],[d,e,f]])
        
        Deprecated in favor of using creation tools for MathObject Matrices 
        Method $matrix->array_ref

Converts Matrix from an ARRAY to an ARRAY reference.

        Method $matrix->list

Converts a Matrix column vector to an ARRAY (list).

        Method $matrix->new_row_matrix
        
        Deprecated -- there are better tools for MathObject Matrices.

Create a row 1 by n matrix from a list. This subroutine appears to be broken

        Method $matrix->proj
        Provides behind the scenes calculations for MathObject Matrix->proj
        Deprecated for direct use in favor of methods of MathObject matrix
        
        Method $matrix->proj_coeff
        Provides behind the scenes calculations for MathObject Matrix->proj_coeff
        Deprecated for direct use in favor of methods of MathObject matrix
        Method $matrix->new_column_matrix

        Create column matrix from an ARRAY reference (list reference)
        
        This method takes an array of column vectors, or an array of arrays,
        and converts them to a matrix where each column is one of the previous
        vectors.
        
        Method $matrix->new_from_col_vecs
        
        Deprecated: The tools for creating MathObjects Matrices are simpler
        Overrides of MatrixReal which allow use of complex entries
        
        Function: cp()
        Provides ability to use complex numbers.
        Method $matrix->copy
        Method $matrix->conj
        Method $matrix->transpose
        Method $matrix->decompose_LR

        Used by MathObjects Matrix for LR decomposition
        Deprecated for direct use in PG problems. 

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