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The operator .
represents noncommutative multiplication and scalar
product. When the operands are 1-column or 1-row matrices a
and
b
, the expression a.b
is equivalent to
sum (a[i]*b[i], i, 1, length(a))
. If a
and b
are not
complex, this is the scalar product, also called the inner product or dot
product, of a
and b
. The scalar product is defined as
conjugate(a).b
when a
and b
are complex;
innerproduct
in the eigen
package provides the complex scalar
product.
When the operands are more general matrices,
the product is the matrix product a
and b
.
The number of rows of b
must equal the number of columns of a
,
and the result has number of rows equal to the number of rows of a
and number of columns equal to the number of columns of b
.
To distinguish .
as an arithmetic operator from the decimal point in a
floating point number, it may be necessary to leave spaces on either side.
For example, 5.e3
is 5000.0
but 5 . e3
is 5
times e3
.
There are several flags which govern the simplification of expressions
involving .
, namely dot0nscsimp
, dot0simp
,
dot1simp
, dotassoc
, dotconstrules
,
dotdistrib
, dotexptsimp
, dotident
, and
dotscrules
.
Next: Matrices, Previous: Introduction to Matrices and Linear Algebra, Up: Introduction to Matrices and Linear Algebra [Contents][Index]