Important: The evalm command has been deprecated.  Matrix algebra expressions involving Matrices such as $A·B$ are evaluated directly, eliminating the need for the additional step of applying evalm.  For additional information, see Linear Algebra Computations in Maple.

The function evalm evaluates an expression involving matrices. It performs any sums, products, or integer powers involving matrices, and will map functions onto matrices.

Note that Maple may perform simplifications before passing the arguments to evalm, and these simplifications may not be valid for matrices. For example, evalm(A^0) will return 1, not the identity matrix.

Unassigned names will be considered either symbolic matrices or scalars depending on their use in an expression.

To indicate non-commutative matrix multiplication, use the operator &*. The matrix product ABC may be entered as $\left(A\&*B\right)\&*C$ or as $\mathrm{\&*}\left(A\,B\,C\right)$, the latter being more efficient. Automatic simplifications such as collecting constants and powers will be applied. Do NOT use the * to indicate purely matrix multiplication, as this will result in an error. The operands of &* must be matrices (or names) with the exception of 0. Unevaluated matrix products are considered to be matrices. The operator &* has the same precedence as the * operator.

Use 0 to denote the matrix or scalar zero. Use $\mathrm{\&*}\left(\right)$ to denote the matrix identity. It may be convenient to use alias(Id=&*()).

If a sum involves a matrix and a Maple constant, the constant will be considered as a constant multiple of the identity matrix. Hence matrix polynomials can be entered in exactly the same fashion as fully expanded scalar polynomials.

$\mathrm{alias}\left(\mathrm{Id}=\mathrm{`\&*`}\left(\right)\right)\:$

$S≔\mathrm{array}\left(\left[\left[1\,2\right]\,\left[3\,4\right]\right]\right)\:$

$T≔\mathrm{array}\left(\left[\left[1\,1\right]\,\left[2\,-1\right]\right]\right)\:$

$\mathrm{evalm}\left(S+2T\right)$

$\left[\begin{array}{cc}3& 4\\ 7& 2\end{array}\right]$

$\mathrm{evalm}\left(S^2\right)$

$\left[\begin{array}{cc}7& 10\\ 15& 22\end{array}\right]$

$\mathrm{evalm}\left(\sin \left(S\right)\right)$

$\left[\begin{array}{cc}\sin \left(1\right)& \sin \left(2\right)\\ \sin \left(3\right)& \sin \left(4\right)\end{array}\right]$

$\mathrm{evalm}\left(S\&*T\right)$

$\left[\begin{array}{cc}5& \mathrm{-1}\\ 11& \mathrm{-1}\end{array}\right]$

$\mathrm{evalm}\left(\left(A\&*B\right)\&*\left(2B\right)-B\&*\mathrm{Id}\right)$

$2\left(A\&*B^2\right)-B\mathrm{Id}$

$\mathrm{evalm}\left(\mathrm{`\&*`}\left(A\,B\,0\right)\right)$

$0$