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Matrix Functions, continued

LQ Factorization. Factors mxn matrix into three matrices:

{ [ [ mXn lowertrapezoidal] ] , [ [ nxn orthogonal] ] ,

[ [ mxm permutation ] ]}.

hQ [matrix)

LSQ

Least Squares. Displays the minimum norm least squares matrix

(or vector).

hSQ [matrix!, matrix2)

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 x 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.

y¡AKEMAT(expression, rows, columns')

Example: MAKEMAT (0,3,3) returns a 3x3 zero matrix,

[[0,0,0], [0,0,0], [0,0,0]].

QR Factorization. Factors an mXn matrix into three matrices:

{ [ [mXm orthogonal] ], [{mXn uppertrapezoidal] ], [[nxn

permutation] ] ).

QR [matrix)

RANK Rank (an integer) of a rectangular matrix.

RANK (mate)

ROWNORM

Row Norm. Finds the maximum value (over all rows) of the sums

of the absolute values of all elements in a row.

ROWNORM (mate)

RREF

Reduced Row-Echelon. Changes a rectangular matrix to its

reduced row-echelon form.

RREF [matrix)

Using Matrices 6-11