Matrix Elements VB-800 Manuel d'utilisateur télécharger pdf (Page 153)

A6.8 Expressions 145

A6.8.5 Multiplicative expressions

The operators .*., *, .*, * , /,and./ group left-to-right and require operands of

arithmetic type. A scalar consists of: int, double or 1 × 1 matrix. These operators

conform to Table A6.3, except for:

left a operator right b result computes

matrix m × n * matrix n × p matrix m × pa

matrix m × n .*. matrix p × q matrix mp × nq a

scalar * matrix n × p matrix n × pab

matrix m × n * scalar matrix m × na

matrix m × n *~ matrix m × p matrix m × np a

b...a

matrix m × n / matrix m × p ≥ m matrix p × n solve bx = a

scalar / matrix m × n matrix m × na/b

matrix m × n / scalar matrix m × na

scalar *.* scalar double a ∗ b

scalar /./ scalar double a/b

This implies that * .*. *~ are the same as .* when one or both arguments are scalar,

and similarly for / and verb./ when the right-hand operand is not a matrix.

Kronecker product is denoted by .*.. If neither operand is a matrix, this is identical

to normal multiplication. Direct (horizontal) multiplication is denoted by * .The

operands must have the same number of rows.

The binary * operator denotes multiplication. If both operands are a matrix and

neither is scalar, this is matrix multiplication and the number of columns of the ﬁrst

operand has to be identical to the number of rows of the second operand.

The .* operator deﬁnes element by element multiplication. It is only different from

* if both operands are a matrix (these must have identical dimensions, however, if one

or both of the arguments is a 1 × 1 matrix, * is equal to .*).

The binary / operator denotes division. If either operand is a scalar, this is identical

to the element-by-element division performed by the ./ operator. If both operands are

matrices, then the result of a/b is x,wherex solves the linear system bx = a; a must

have the same number of rows as a. (Note the potential for confusion: more logical

would be to solve xb = a by a/b.) If b has the same number of columns as a,the

system is solved by a LU decomposition with pivoting; if b has more columns, it is

equivalent to a least squares problem (b

bx = b

a which is solved by the Choleski

decomposition of b

b (rather than the QR decomposition of b).

The ./ operator deﬁnes element by element division. If either argument is not a

matrix, this is identical to normal division. It is only different from / if both operands

are a non-scalar matrix, then both matrices must have identical dimensions.

Note that the result of dividing two integers is a double (3 / 2 gives 1.5). Multipli-

cation of two integers also returns a double.

Notice the difference between 2./ m2 and 2./m2. In the ﬁrst case, the dot is

interpreted as part of the real number 2., whereas in the second case it is part of the

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