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