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• To indicate non-commutative matrix multiplication, use the operator &*. The matrix product ABC
may be entered as A &* B &* C or as &*(A,B,C), 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 &*() to denote the matrix identity. It may be
convenient to use alias(Id=&*()).
> alias(Id=&*()):
> S := array([[1,2],[3,4]]):
> T := array([[1,1],[2,-1]]):
> evalm(S+2*T);
⎡3
4⎤
⎢ ⎥
⎣7
2⎦
> evalm(S^2);
⎡ 7 10⎤
⎢ ⎥
⎣15
22⎦
> evalm(S &* T);
⎡ 5 −1⎤
⎢ ⎥
⎣11
−1⎦
> evalm(T+Id);
⎡2
1⎤
⎢ ⎥
⎣2
0⎦
11.5 Advanced Maple
11.5.1 Manipulating Expressions
You can examine parts of expressions by using the standard Maple library functions designed to
categorize them or to pull them apart: type, whattype, op, and nops are some of those functions.
To look at the i-th part of an expression, you use op(i, expression), where i evaluates to a nonnegative
integer.
Example:
> e1 := op1 + op2 + op3:
> e2 := op1 * op2 * sin(op3):
> op(2, e1);
op2
> op(3, e2);
sin(op3)
As you can see, the operands of the expression are returned, not the operators that connect them.
This is because Maple categorizes expressions into "types". For instance, "a+b+c" is of type "+" and
has three operands; "a+b*c" is also of type "+" and has only two operands, one of which is of type "*"
and itself has two operands. The whattype function tells you the type of an expression; type is a
boolean test that allows you to check for a particular type of expression. For example:
> whattype(e1);
+
> whattype(e2);
*
> type(e1+e2, `+`);
true
> type(expand(e1*e2),`+`);
117