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<a name="Dot"></a>
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<p>
Next: <a href="maxima_116.html#Matrices" accesskey="n" rel="next">Matrices</a>, Previous: <a href="maxima_114.html#Introduction-to-Matrices-and-Linear-Algebra" accesskey="p" rel="previous">Introduction to Matrices and Linear Algebra</a>, Up: <a href="maxima_114.html#Introduction-to-Matrices-and-Linear-Algebra" accesskey="u" rel="up">Introduction to Matrices and Linear Algebra</a> &nbsp; [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_368.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Dot-1"></a>
<h4 class="subsection">23.1.1 Dot</h4>

<p>The operator <code>.</code> represents noncommutative multiplication and scalar
product.  When the operands are 1-column or 1-row matrices <code>a</code> and
<code>b</code>, the expression <code>a.b</code> is equivalent to
<code>sum (a[i]*b[i], i, 1, length(a))</code>.  If <code>a</code> and <code>b</code> are not
complex, this is the scalar product, also called the inner product or dot
product, of <code>a</code> and <code>b</code>.  The scalar product is defined as
<code>conjugate(a).b</code> when <code>a</code> and <code>b</code> are complex;
<code><a href="maxima_119.html#innerproduct">innerproduct</a></code> in the <code>eigen</code> package provides the complex scalar
product.
</p>
<p>When the operands are more general matrices,
the product is the matrix product <code>a</code> and <code>b</code>.
The number of rows of <code>b</code> must equal the number of columns of <code>a</code>,
and the result has number of rows equal to the number of rows of <code>a</code>
and number of columns equal to the number of columns of <code>b</code>.
</p>
<p>To distinguish <code>.</code> 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, <code>5.e3</code> is <code>5000.0</code> but <code>5 . e3</code> is <code>5</code>
times <code>e3</code>.
</p>
<p>There are several flags which govern the simplification of expressions
involving <code>.</code>, namely <code><a href="maxima_119.html#dot0nscsimp">dot0nscsimp</a></code>, <code><a href="maxima_119.html#dot0simp">dot0simp</a></code>,<!-- /@w -->
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<code><a href="maxima_119.html#dotdistrib">dotdistrib</a></code>, <code><a href="maxima_119.html#dotexptsimp">dotexptsimp</a></code>, <code><a href="maxima_119.html#dotident">dotident</a></code>, and
<code><a href="maxima_119.html#dotscrules">dotscrules</a></code>.
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Next: <a href="maxima_116.html#Matrices" accesskey="n" rel="next">Matrices</a>, Previous: <a href="maxima_114.html#Introduction-to-Matrices-and-Linear-Algebra" accesskey="p" rel="previous">Introduction to Matrices and Linear Algebra</a>, Up: <a href="maxima_114.html#Introduction-to-Matrices-and-Linear-Algebra" accesskey="u" rel="up">Introduction to Matrices and Linear Algebra</a> &nbsp; [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_368.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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