Conformable matrix

<h2 id="examples">Examples</h2>
<ul><li>If two matrices have the same dimensions (number of rows and number of columns), they are <i>conformable for addition</i>.</li>
<li>Multiplication of two matrices is defined if and only if the number of columns of the left matrix is the same as the number of rows of the right matrix. That is, if A is an <i>m</i> × <i>n</i> matrix and B is an <i>s</i> × <i>p</i> matrix, then <i>n</i> needs to be equal to <i>s</i> for the matrix product AB to be defined. In this case, we say that A and B are <i>conformable for multiplication</i> (in that sequence).</li>
<li>Since squaring a matrix involves multiplying it by itself (A2 = AA) a matrix must be <i>m</i> × <i>m</i> (that is, it must be a <a href="/facts/Square_matrix/5TP9mNNn">square matrix</a>) to be <i>conformable for squaring</i>. Thus for example only a square matrix can be <a href="/facts/Idempotent_matrix/88Es7cEn">idempotent</a>.</li>
<li>Only a square matrix is <i>conformable for <a href="/facts/Matrix_inversion/fPqXk3V8">matrix inversion</a></i>. However, the <a href="/facts/Moore%E2%80%93Penrose_pseudoinverse/CU73tntq">Moore–Penrose pseudoinverse</a> and other <a href="/facts/Generalized_inverse/4xVKDIAp">generalized inverses</a> do not have this requirement.</li>
<li>Only a square matrix is <i>conformable for <a href="/facts/Matrix_exponentiation/WID5cG2g">matrix exponentiation</a></i>.</li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Linear_algebra/8VaB4VWk">Linear algebra</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Cullen, Charles G. (1990). Matrices and linear transformations (2nd ed.). New York: Dover. ISBN 0486663280. <a href="0486663280" target="_blank">0486663280</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
</ol>

Conformable matrix open-in-new

Conformable matrix