This seems like a very basic question that I should know the answer to, but in my image processing class, my teacher explained that a basis set of images(matrices) are orthonormal.(adsbygoogle = window.adsbygoogle || []).push({});

He said that the DOT product between two basis images (in this case two 2x2 matrices) is 0. so, for example

\begin{equation}

\begin{bmatrix}

a & b\\

c & d

\end{bmatrix}

\cdot

\begin{bmatrix}

e & f\\

g & h

\end{bmatrix}

=0

\end{equation}

I don't understand how this can be. I always thought it gave another matrix, and not a direct value:

\begin{equation}

\begin{bmatrix}

a & b\\

c & d

\end{bmatrix}

\cdot

\begin{bmatrix}

e & f\\

g & h

\end{bmatrix}

=

\begin{bmatrix}

ae+bg & af+bh\\

ce+dg & cf+dh

\end{bmatrix}

\end{equation}

Can someone help me out? It would be unbelieveably helpful,

Thanks!

Owen.

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# Dot Product 2x2 Matrix

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