Manuals/calci/HADAMARDPRODUCT

HADAMARDPRODUCT (a,b)

$a$ and $b$ are any two matrices.

Description

This function shows the value of the Hadamard product.
In $HADAMARDPRODUCT(a,b)$ , $a$ and $b$ are two matrices.
Hadamard product is also called Schur product or entrywise product.
The Hadamard product is associative,commutative and distributive.
This product is the multiplied value of the each corresponding entries with the given two same dimension matrices.
Hadamard product is defined by,For two matrices, A and B of the same dimension mxn, the Hadamard product $A\circ B$ , is a matrix, of the same dimension as the operands, with elements given by:

$(A\circ B)_{i,j}=(A)_{i,j}(B)_{i,j}$

Hadamard Product of order 2 is calculated by:

${\begin{pmatrix}a_{11}&a_{12}\\a_{21}&a_{22}\end{pmatrix}}$ $\circ$ ${\begin{pmatrix}b_{11}&b_{12}\\b_{21}&b_{22}\end{pmatrix}}$ = ${\begin{pmatrix}a_{11}b_{11}&a_{12}b_{12}\\a_{21}b_{21}&a_{22}b_{22}\end{pmatrix}}$