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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]