- #1

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## Main Question or Discussion Point

Suppose you have a matrix A:

[tex]

\left(

\begin{array}{ccc}

a_{1,1} & a_{1,2} & a_{1,3} \\

a_{2,1} & a_{2,2} & a_{2,3} \\

a_{3,1} & a_{3,2} & a_{3,3}

\end{array}

\right)

[/tex]

And a matrix B:

[tex]

\left(

\begin{array}{ccc}

b_{1,1} & b_{1,2} & b_{1,3} \\

b_{2,1} & b_{2,2} & b_{2,3} \\

b_{3,1} & b_{3,2} & b_{3,3}

\end{array}

\right)

[/tex]

I want a product [itex]A \star B[/itex] that would result in:

[tex]

\left(

\begin{array}{ccc}

a_{1,1} b_{1,1} & a_{1,2} b_{1,2} & a_{1,3} b_{1,3} \\

a_{2,1} b_{2,1} & a_{2,2} b_{2,2} & a_{2,3} b_{2,3} \\

a_{3,1} b_{3,1} & a_{3,2} b_{3,2} & a_{3,3} b_{3,3}

\end{array}

\right)

[/tex]

Does such a product exist? What would be the name of it?

[tex]

\left(

\begin{array}{ccc}

a_{1,1} & a_{1,2} & a_{1,3} \\

a_{2,1} & a_{2,2} & a_{2,3} \\

a_{3,1} & a_{3,2} & a_{3,3}

\end{array}

\right)

[/tex]

And a matrix B:

[tex]

\left(

\begin{array}{ccc}

b_{1,1} & b_{1,2} & b_{1,3} \\

b_{2,1} & b_{2,2} & b_{2,3} \\

b_{3,1} & b_{3,2} & b_{3,3}

\end{array}

\right)

[/tex]

I want a product [itex]A \star B[/itex] that would result in:

[tex]

\left(

\begin{array}{ccc}

a_{1,1} b_{1,1} & a_{1,2} b_{1,2} & a_{1,3} b_{1,3} \\

a_{2,1} b_{2,1} & a_{2,2} b_{2,2} & a_{2,3} b_{2,3} \\

a_{3,1} b_{3,1} & a_{3,2} b_{3,2} & a_{3,3} b_{3,3}

\end{array}

\right)

[/tex]

Does such a product exist? What would be the name of it?