Difference between revisions of "Manuals/calci/HADAMARDPRODUCT"
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| − | HADAMARDPRODUCT | + | <div style="font-size:30px">'''HADAMARDPRODUCT (a,b)'''</div><br/> |
| + | *<math> a</math> and <math>b </math> are any two matrices. | ||
| + | |||
| + | ==Description== | ||
| + | *This function shows the value of the Hadamard product. | ||
| + | *In <math>HADAMARDPRODUCT(a,b)</math>,<math>a</math> and <math>b</math> 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, <math> A\circ B</math, is a matrix, of the same dimension as the operands, with elements given by: | ||
| + | <math>(A \circ B)_{i,j}=(A)_{i,j}(B)_{i,j} </math> | ||
| + | *Hadamard Product of order 2 is calculated by: | ||
| + | <math>\begin{pmatrix} | ||
| + | a_{11} & a_{12} \\ | ||
| + | a_{21} & a_{22} | ||
| + | \end{pmatrix}</math><math>\circ</math> | ||
| + | <math>\begin{pmatrix} | ||
| + | b_{11} & b_{12} \\ | ||
| + | b_{21} & b_{22} | ||
| + | \end{pmatrix}</math> = <math>\begin{pmatrix} | ||
| + | a_{11}b_{11} & a_{12}b_{12} \\ | ||
| + | a_{21}b_{21} & a_{22}b_{22} | ||
| + | \end{pmatrix}</math> | ||
Revision as of 14:25, 6 June 2017
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b } are any two matrices.
Description
- This function shows the value of the Hadamard product.
- In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle HADAMARDPRODUCT(a,b)} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and 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, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A\circ B</math, is a matrix, of the same dimension as the operands, with elements given by: <math>(A \circ B)_{i,j}=(A)_{i,j}(B)_{i,j} }
- Hadamard Product of order 2 is calculated by:
are two matrices.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \circ} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{pmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{pmatrix}} = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{pmatrix} a_{11}b_{11} & a_{12}b_{12} \\ a_{21}b_{21} & a_{22}b_{22} \end{pmatrix}}