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<p>inverse.</p>

<p><big> Motivation </big></p>
 <p>Consider the <a href="page.php?w=System_of_linear_equations">linear system</a></p>

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<p>where  is an  matrix and  the <a href="page.php?w=column_space">column space</a> of .  If  and  is <a href="page.php?w=Invertible_matrix">nonsingular</a> then  will be the solution of the system.  Note that, if  is nonsingular, then</p>

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:</p>

<p>Now suppose  is rectangular (), or square and singular. Then we need a right candidate  of order  such that for all </p>

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:</p>

<p>That is,  is a solution</p><p>
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