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15-12 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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