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<h3 class="section">8.3 Arithmetic Operators</h3>
<p><a name="index-arithmetic-operators-457"></a><a name="index-operators_002c-arithmetic-458"></a><a name="index-addition-459"></a><a name="index-subtraction-460"></a><a name="index-multiplication-461"></a><a name="index-matrix-multiplication-462"></a><a name="index-division-463"></a><a name="index-quotient-464"></a><a name="index-negation-465"></a><a name="index-unary-minus-466"></a><a name="index-exponentiation-467"></a><a name="index-transpose-468"></a><a name="index-Hermitian-operator-469"></a><a name="index-transpose_002c-complex_002dconjugate-470"></a><a name="index-complex_002dconjugate-transpose-471"></a>
The following arithmetic operators are available, and work on scalars
and matrices.
<dl>
<dt><var>x</var><code> + </code><var>y</var><dd><a name="index-g_t_002b-472"></a>Addition. If both operands are matrices, the number of rows and columns
must both agree. If one operand is a scalar, its value is added to
all the elements of the other operand.
<br><dt><var>x</var><code> .+ </code><var>y</var><dd><a name="index-g_t_002e_002b-473"></a>Element by element addition. This operator is equivalent to <code>+</code>.
<br><dt><var>x</var><code> - </code><var>y</var><dd><a name="index-g_t_002d-474"></a>Subtraction. If both operands are matrices, the number of rows and
columns of both must agree.
<br><dt><var>x</var><code> .- </code><var>y</var><dd>Element by element subtraction. This operator is equivalent to <code>-</code>.
<br><dt><var>x</var><code> * </code><var>y</var><dd><a name="index-g_t_002a-475"></a>Matrix multiplication. The number of columns of <var>x</var> must agree
with the number of rows of <var>y</var>.
<br><dt><var>x</var><code> .* </code><var>y</var><dd><a name="index-g_t_002e_002a-476"></a>Element by element multiplication. If both operands are matrices, the
number of rows and columns must both agree.
<br><dt><var>x</var><code> / </code><var>y</var><dd><a name="index-g_t_002f-477"></a>Right division. This is conceptually equivalent to the expression
<pre class="example"> (inverse (y') * x')'
</pre>
<p class="noindent">but it is computed without forming the inverse of <var>y'</var>.
<p>If the system is not square, or if the coefficient matrix is singular,
a minimum norm solution is computed.
<br><dt><var>x</var><code> ./ </code><var>y</var><dd><a name="index-g_t_002e_002f-478"></a>Element by element right division.
<br><dt><var>x</var><code> \ </code><var>y</var><dd><a name="index-g_t_005c-479"></a>Left division. This is conceptually equivalent to the expression
<pre class="example"> inverse (x) * y
</pre>
<p class="noindent">but it is computed without forming the inverse of <var>x</var>.
<p>If the system is not square, or if the coefficient matrix is singular,
a minimum norm solution is computed.
<br><dt><var>x</var><code> .\ </code><var>y</var><dd><a name="index-g_t_002e_005c-480"></a>Element by element left division. Each element of <var>y</var> is divided
by each corresponding element of <var>x</var>.
<br><dt><var>x</var><code> ^ </code><var>y</var><dt><var>x</var><code> ** </code><var>y</var><dd><a name="index-g_t_002a_002a-481"></a><a name="index-g_t_005e-482"></a>Power operator. If <var>x</var> and <var>y</var> are both scalars, this operator
returns <var>x</var> raised to the power <var>y</var>. If <var>x</var> is a scalar and
<var>y</var> is a square matrix, the result is computed using an eigenvalue
expansion. If <var>x</var> is a square matrix, the result is computed by
repeated multiplication if <var>y</var> is an integer, and by an eigenvalue
expansion if <var>y</var> is not an integer. An error results if both
<var>x</var> and <var>y</var> are matrices.
<p>The implementation of this operator needs to be improved.
<br><dt><var>x</var><code> .^ </code><var>y</var><br><dt><var>x</var><code> .** </code><var>y</var><dd><a name="index-g_t_002e_002a_002a-483"></a><a name="index-g_t_002e_005e-484"></a>Element by element power operator. If both operands are matrices, the
number of rows and columns must both agree.
<br><dt><code>-</code><var>x</var><dd><a name="index-g_t_002d-485"></a>Negation.
<br><dt><code>+</code><var>x</var><dd><a name="index-g_t_002b-486"></a>Unary plus. This operator has no effect on the operand.
<br><dt><var>x</var><code>'</code><dd><a name="index-g_t_0027-487"></a>Complex conjugate transpose. For real arguments, this operator is the
same as the transpose operator. For complex arguments, this operator is
equivalent to the expression
<pre class="example"> conj (x.')
</pre>
<br><dt><var>x</var><code>.'</code><dd><a name="index-g_t_002e_0027-488"></a>Transpose.
</dl>
<p>Note that because Octave's element by element operators begin with a
‘<samp><span class="samp">.</span></samp>’, there is a possible ambiguity for statements like
<pre class="example"> 1./m
</pre>
<p class="noindent">because the period could be interpreted either as part of the constant
or as part of the operator. To resolve this conflict, Octave treats the
expression as if you had typed
<pre class="example"> (1) ./ m
</pre>
<p class="noindent">and not
<pre class="example"> (1.) / m
</pre>
<p class="noindent">Although this is inconsistent with the normal behavior of Octave's
lexer, which usually prefers to break the input into tokens by
preferring the longest possible match at any given point, it is more
useful in this case.
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