Register to reply

Matrix multiplication vs dot product

by jabers
Tags: dot product, matrices
Share this thread:
jabers
#1
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?

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.
Phys.Org News Partner Science news on Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
sharks
#2
May21-12, 10:19 AM
PF Gold
sharks's Avatar
P: 836
Don't confuse dot product of matrix with vectors. The second product is correct.
jabers
#3
May21-12, 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?

deluks917
#4
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).
JoshMaths
#5
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

\begin{pmatrix}
a & b
\end{pmatrix}dot\begin{pmatrix}
e \\
g
\end{pmatrix}

and so on for the rest of the positions.


Register to reply

Related Discussions
System under matrix addition (+) and matrix multiplication (.) is a field Introductory Physics Homework 1
Matrix Multiplication and Rank of Matrix General Math 2
Matrix multiplication preserve order Block matrix Linear & Abstract Algebra 2
Matrix Multiplication and Algebraic Properties of Matrix Operations Calculus & Beyond Homework 2
Matrix multiplication and the dot product Calculus & Beyond Homework 9