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18-12 Matrices
LU LU Decomposition. Factors a square matrix into three
matrices:
{[[lowertriangular]],[[uppertriangular]],[[permutation]]}
The uppertriangular has ones on its diagonal.
LU(matrix)
MAKEMAT Make Matrix. Creates a matrix of dimension rows ×
columns, using expression to calculate each element. If
expression contains the variables I and J, then the
calculation for each element substitutes the current row
number for I and the current column number for J.
MAKEMAT(expression, rows, columns)
Example
MAKEMAT(0,3,3) returns a 3×3 zero matrix,
[[0,0,0],[0,0,0],[0,0,0]].
QR QR Factorization. Factors an m×n matrix into three
matrices: {[[m×m orthogonal]],[[m×n
uppertrapezoidal]],[[n×n permutation]]}.
QR(matrix)
RANK Rank of a rectangular matrix.
RANK(matrix)
ROWNORM Row Norm. Finds the maximum value (over all rows) for
the sums of the absolute values of all elements in a row.
ROWNORM(matrix)
RREF Reduced-Row Echelon Form. Changes a rectangular
matrix to its reduced row-echelon form.
RREF(matrix)
SCHUR Schur Decomposition. Factors a square matrix into two
matrices. If matrix is real, then the result is
{[[orthogonal]],[[upper-quasi triangular]]}.
If matrix is complex, then the result is
{[[unitary]],[[upper-triangular]]}.
SCHUR(matrix)
SIZE Dimensions of matrix. Returned as a list: {rows,columns}.
SIZE(matrix)
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