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Matrix multiplication vs dot product 
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#1
May2112, 09:25 AM

P: 15

What is the difference between matrix multiplication and the dot product of two matrices? Is there a difference?
If, [tex]A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}[/tex] and [tex]B = \begin{pmatrix} e & f \\ g & h \end{pmatrix}[/tex] then does [tex] {\mathbf{A} \cdot \mathbf{B}} = \begin{pmatrix} ae & bf \\ cg & dh \end{pmatrix}[/tex] and [tex]AB = \begin{pmatrix} ae + bg & af + bh \\ ce + dg & cf + dh \end{pmatrix}[/tex] ? Is this correct? Any help would be appreciated. 


#2
May2112, 10:19 AM

PF Gold
P: 836

Don't confuse dot product of matrix with vectors. The second product is correct.



#3
May2112, 10:24 AM

P: 15

so,
[tex]{\mathbf{A} \cdot \mathbf{B}} = AB = \begin{pmatrix} ae + bg & af + bh \\ ce + dg & cf + dh \end{pmatrix}[/tex] With matrices the dot product means that you need to multiply the matrices? Correct? 


#4
May2112, 11:35 AM

P: 367

Matrix multiplication vs dot product
Usually the "dot product" of two matrices is not defined. I think a "dot product" should output a real (or complex) number. So one definition of A[itex]\bullet[/itex]B is ae + bf + cg + df. This is thinking of A, B as elements of R^4. If we want our dot product to be a bilinear map into R this is how we need to define it (up to multiplication by a constant).



#5
May2112, 01:33 PM

P: 31

You should view AB as a collection of dot products ie.
ab_{11} (top left of AB) can be described as the dot product of \begin{pmatrix} a & b \end{pmatrix}dot\begin{pmatrix} e \\ g \end{pmatrix} and so on for the rest of the positions. 


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