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<A NAME=Linear_Algebra_package>

<TITLE>Linear_Algebra_package</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>LINEAR ALGEBRA PACKAGE</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>introduction</B><P>
<P>
 
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<P>
This section briefly describes what's available in the Linear Algebra 
package. 
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<P>
Note on examples: In the examples throughout this 
document, the matrix A will be 
<P><PRE><TT>
     [1  2  3]
     [4  5  6]
     [7  8  9].
</TT></PRE><P><P>
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The functions can be divided into four categories: 
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Basic matrix handling 
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<A HREF=r37_0572.html>add_columns</A>, 
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<A HREF=r37_0573.html>add_rows</A>, 
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<A HREF=r37_0574.html>add_to_columns</A>, 
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<A HREF=r37_0575.html>add_to_rows</A>, 
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<A HREF=r37_0576.html>augment_columns</A>, 
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<A HREF=r37_0580.html>char_poly</A>, 
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<A HREF=r37_0583.html>column_dim</A>, 
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<A HREF=r37_0585.html>copy_into</A>, 
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<A HREF=r37_0586.html>diagonal</A>, 
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<A HREF=r37_0587.html>extend</A>, 
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<A HREF=r37_0588.html>find_companion</A>, 
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<A HREF=r37_0589.html>get_columns</A>, 
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<A HREF=r37_0590.html>get_rows</A>, 
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<A HREF=r37_0592.html>hermitian_tp</A>, 
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<A HREF=r37_0599.html>matrix_augment</A>, 
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<A HREF=r37_0601.html>matrix_stack</A>, 
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<A HREF=r37_0602.html>minor</A>, 
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<A HREF=r37_0603.html>mult_columns</A>, 
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<A HREF=r37_0604.html>mult_rows</A>, 
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<A HREF=r37_0605.html>pivot</A>, 
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<A HREF=r37_0608.html>remove_columns</A>, 
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<A HREF=r37_0609.html>remove_rows</A>, 
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<A HREF=r37_0610.html>row_dim</A>, 
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<A HREF=r37_0611.html>rows_pivot</A>, 
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<A HREF=r37_0614.html>stack_rows</A>, 
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<A HREF=r37_0615.html>sub_matrix</A>, 
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<A HREF=r37_0617.html>swap_columns</A>, 
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<A HREF=r37_0618.html>swap_entries</A>, 
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<A HREF=r37_0619.html>swap_rows</A>. 
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Constructors -- functions that create matrices 
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<A HREF=r37_0577.html>band_matrix</A>, 
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<A HREF=r37_0578.html>block_matrix</A>, 
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<A HREF=r37_0579.html>char_matrix</A>, 
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<A HREF=r37_0582.html>coeff_matrix</A>, 
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<A HREF=r37_0584.html>companion</A>, 
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<A HREF=r37_0593.html>hessian</A>, 
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<A HREF=r37_0594.html>hilbert</A>, 
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<A HREF=r37_0595.html>jacobian</A>, 
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<A HREF=r37_0596.html>jordan_block</A>, 
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<A HREF=r37_0598.html>make_identity</A>, 
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<A HREF=r37_0607.html>random_matrix</A>, 
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<A HREF=r37_0621.html>toeplitz</A>, 
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<A HREF=r37_0622.html>vandermonde</A>. 
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High level algorithms 
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<A HREF=r37_0580.html>char_poly</A>, 
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<A HREF=r37_0581.html>cholesky</A>, 
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<A HREF=r37_0591.html>gram_schmidt</A>, 
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<A HREF=r37_0597.html>lu_decom</A>, 
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<A HREF=r37_0606.html>pseudo_inverse</A>, 
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<A HREF=r37_0612.html>simplex</A>, 
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<A HREF=r37_0616.html>svd</A>. 
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Normal Forms 
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There is a separate package, NORMFORM, for computing 
the following matrix normal forms in REDUCE: 
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<A HREF=r37_0624.html>smithex</A>, 
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<A HREF=r37_0625.html>smithex_int</A>, 
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<A HREF=r37_0626.html>frobenius</A>, 
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<A HREF=r37_0627.html>ratjordan</A>, 
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<A HREF=r37_0628.html>jordansymbolic</A>, 
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<A HREF=r37_0629.html>jordan</A>. 
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Predicates 
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<A HREF=r37_0600.html>matrixp</A>, 
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<A HREF=r37_0613.html>squarep</A>, 
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<P>

<A HREF=r37_0620.html>symmetricp</A>. 
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