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    <p>First, let's declare the <em>symbolics</em> easier using <a href="http://www.mathworks.com/help/symbolic/sym.html" rel="nofollow"><code>sym</code></a>:</p> <pre><code>T = sym('T%d%d', [4 4]); A = sym('A%d%d', [4 4]); L = sym('L', [4 1]); </code></pre> <p>There are several problems with the original code; <strong>1.</strong> <code>f</code> is being replaced in each inner iteration. <strong>2.</strong> The inner result should be scalar and thus <code>I</code> must not appear there. (Note that you can also define <code>I</code> like <a href="http://www.mathworks.com/help/matlab/ref/eye.html" rel="nofollow"><code>eye(4)</code></a> instead of writing it manually.)</p> <p>Here is the corrected version:</p> <pre><code>f = cell(4,1); % Initialize equation system for r = 1:k for k = 1:4 for i = 1:4 f{r}(i,k) = T(i,k) * A(r,k); end end f{r} = f{r} - L(r)*diag(A(r,:)); end </code></pre> <p><code>f{i}</code> would be the <code>ith</code> slice.</p> <p><strong>Note</strong>: As @Schorsch pointed out (and Matlab also shows a <em>warning</em>) always try to use another variable name other than <code>i</code> (or <code>j</code>), since they represent the <a href="http://www.mathworks.com/help/matlab/ref/i.html" rel="nofollow"><em>imaginary unit</em></a>.</p> <p>Just for fun you can use <a href="http://www.mathworks.com/help/matlab/ref/repmat.html" rel="nofollow"><code>repmat</code></a> to remove the two inner loops:</p> <pre><code>for r = 1:4 f{r} = T .* repmat(A(r,:), [4 1]) - L(r)*diag(A(r,:)); end </code></pre>
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    1. CO+1 for the explanations and for introducing `repmat` to eliminate some of the loops. One additional remark, `i` (and `j` for that matter) should not be used as iterators because the are also the [imaginary unit](http://www.mathworks.com/help/matlab/ref/i.html) in Matlab.
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    2. COWell that's true I will add a comment there, but I was just trying to keep the original code as far as possible.
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    3. COI understand that and agree with it. It was just something I wanted to mention for completeness' sake.
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