# Matrix multiplication vs dot product

by jabers
Tags: dot product, matrices
 P: 15 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.
 P: 15 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).