(maxima.info)Dot

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23.1.1 Dot
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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'.