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Matrix multiplication vs dot product

by jabers
Tags: dot product, matrices
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May21-12, 09:25 AM
P: 15
What is the difference between matrix multiplication and the dot product of two matrices? Is there a difference?


[tex]A =
a & b \\
c & d


[tex]B =
e & f \\
g & h

then does
{\mathbf{A} \cdot \mathbf{B}} =
ae & bf \\
cg & dh


[tex]AB =
ae + bg & af + bh \\
ce + dg & cf + dh

? Is this correct? Any help would be appreciated.
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May21-12, 10:19 AM
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sharks's Avatar
P: 836
Don't confuse dot product of matrix with vectors. The second product is correct.
May21-12, 10:24 AM
P: 15

[tex]{\mathbf{A} \cdot \mathbf{B}} = AB =
ae + bg & af + bh \\
ce + dg & cf + dh

With matrices the dot product means that you need to multiply the matrices? Correct?

May21-12, 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 bi-linear map into R this is how we need to define it (up to multiplication by a constant).
May21-12, 01:33 PM
P: 31
You should view AB as a collection of dot products ie.
ab11 (top left of AB) can be described as the dot product of

a & b
e \\

and so on for the rest of the positions.

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