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These follow the normal rules of matrix algebra as defined by the following syntax:
\(\langle \)matrix expression\(\rangle \) | \(\longrightarrow \) | mat \(\langle \)matrix description\(\rangle \)\(\ \mid \ \)\(\langle \)matrix variable\(\rangle \)\(\ \mid \ \) |
\(\langle \)scalar expression\(\rangle \)* \(\langle \)matrix expression\(\rangle \)\(\ \mid \ \) |
||
\(\langle \)matrix expression\(\rangle \)* \(\langle \)matrix expression\(\rangle \)\(\ \mid \ \) |
||
\(\langle \)matrix expression\(\rangle \)+ \(\langle \)matrix expression\(\rangle \)\(\ \mid \ \) |
||
\(\langle \)matrix expression\(\rangle \)^ \(\langle \)integer\(\rangle \)\(\ \mid \ \) |
||
\(\langle \)matrix expression\(\rangle \)/ \(\langle \)matrix expression\(\rangle \) |
Sums and products of matrix expressions must be of compatible size; otherwise an error
will result during their evaluation. Similarly, only square matrices may be raised to a
power. A negative power is computed as the inverse of the matrix raised to the
corresponding positive power. a/b
is interpreted as a*b^(-1)
.
Examples:
Assuming x
and y
have been declared as matrices, the following are matrix
expressions
y y^2*x-3*y^(-2)*x y + mat((1,a),(b,c))/2
The computation of the quotient of two matrices normally uses a two-step
elimination method due to Bareiss. An alternative method using Cramer’s method is
also available. This is usually less efficient than the Bareiss method unless the
matrices are large and dense, although we have no solid statistics on this as
yet. To use Cramer’s method instead, the switch cramer
should be turned
on.
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