LINEAR ALGEBRA PACKAGE _ _ _ _ _ _ _ _ _ _ _ _ introduction

This section briefly describes what's available in the Linear Algebra package.

Note on examples: In the examples throughout this document, the matrix A will be

     [1  2  3]
     [4  5  6]
     [7  8  9].

The functions can be divided into four categories:

Basic matrix handling

add_columns,

add_rows,

add_to_columns,

add_to_rows,

augment_columns,

char_poly,

column_dim,

copy_into,

diagonal,

extend,

find_companion,

get_columns,

get_rows,

hermitian_tp,

matrix_augment,

matrix_stack,

minor,

mult_columns,

mult_rows,

pivot,

remove_columns,

remove_rows,

row_dim,

rows_pivot,

stack_rows,

sub_matrix,

swap_columns,

swap_entries,

swap_rows.

Constructors -- functions that create matrices

band_matrix,

block_matrix,

char_matrix,

coeff_matrix,

companion,

hessian,

hilbert,

jacobian,

jordan_block,

make_identity,

random_matrix,

toeplitz,

vandermonde.

High level algorithms

char_poly,

cholesky,

gram_schmidt,

lu_decom,

pseudo_inverse,

simplex,

svd.

Normal Forms

There is a separate package, NORMFORM, for computing the following matrix normal forms in REDUCE:

smithex,

smithex_int,

frobenius,

ratjordan,

jordansymbolic,

jordan.

Predicates

matrixp,

squarep,

symmetricp.