matrix multiplication vs dot product

by jabers
Tags: dot product, matrices
 P: 14 What is the difference between matrix multiplication and the dot product of two matrices? Is there a difference? If, $$A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$$ and $$B = \begin{pmatrix} e & f \\ g & h \end{pmatrix}$$ then does $${\mathbf{A} \cdot \mathbf{B}} = \begin{pmatrix} ae & bf \\ cg & dh \end{pmatrix}$$ and $$AB = \begin{pmatrix} ae + bg & af + bh \\ ce + dg & cf + dh \end{pmatrix}$$ ? Is this correct? Any help would be appreciated.
 PF Gold P: 836 Don't confuse dot product of matrix with vectors. The second product is correct.
 P: 14 so, $${\mathbf{A} \cdot \mathbf{B}} = AB = \begin{pmatrix} ae + bg & af + bh \\ ce + dg & cf + dh \end{pmatrix}$$ With matrices the dot product means that you need to multiply the matrices? Correct?
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$\bullet$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).
 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 \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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