MATLAB: What is the simplest way to get an element of an matrix multiplication?

Question

What is the simplest way to get an element of an matrix multiplication?

Assume $A$ and $B$ are $n\times n$ matricies. And $1\le i\le n$ and $1\le j\le n$ are inidicies

I tried $(A*B)(i,j)$ but this is no valid MATLAB syntax.

Sure an other way is $C=A*B$ and then $C(i,j)$ but this to complex and long for me.

Is there a trick to do that in a simple and compact way?

Thanks

score 1 · Accepted Answer · answered Sep 09 '14 at 13:44

1

If $A$ and $B$ are $n \times n$ real matrices with $A=(a_{i,j})_{1 \leq i,j \leq n}$ and $B = (b_{i,j})_{1 \leq i,j \leq n}$, for a given $(i,j) \in \lbrace 1,\ldots,n \rbrace^{2}$,

$$ \big( AB \big)_{i,j} = \sum_{k=1}^{n} a_{i,k}b_{k,j} $$

As a consequence, you could try : dot(A(i,:)',B(:,j)) in MATLAB.

answered Sep 09 '14 at 13:44

pitchounet

6,576

And of course the vector dot product with dot is equivalent to A(i,:)'*B(:,j). – horchler Sep 09 '14 at 22:56
Careful with that '. It should be .'. The distinction matters if the matrix is complex – Luis Mendo Jan 28 '15 at 16:43
@LuisMendo : Thank you for your comment. I didn't know that ! – pitchounet Jan 28 '15 at 17:38
@jibounet Many people don't, and then they get problems due to the unexpected complex-conjugate :-) – Luis Mendo Jan 28 '15 at 17:41

MATLAB: What is the simplest way to get an element of an matrix multiplication?

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