Difference between revisions of "Manuals/calci/IDEMPOTENT"
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| − | <div style="font-size:30px">'''IDEMPOTENT'''</div><br/> | + | <div style="font-size:30px">'''MATRIX("IDEMPOTENT",order)'''</div><br/> |
| + | *<math>order</math> is the size of the Idempotent matrix. | ||
| + | |||
| + | ==Description== | ||
| + | *This function is showing the idempotent matrix of order 3. | ||
| + | *An idempotent matrix is a matrix which, when multiplied by itself, is getting the same matrix. | ||
| + | *i.e.,A square matrix K is said to be idempotent if <math>K^2=K</math>. | ||
| + | *The properties of idempotent matrix is: | ||
| + | # <math>K^r=K</math> for r being a positive integer. | ||
| + | # <math>I-K</math> is idempotent. | ||
| + | # If <math>K_1</math> and <math>K_2</math> are idempotent matrices and <math>K_1K_2 =K_2K_1</math>. Then <math>K_1K_2</math> is idempotent. | ||
| + | |||
| + | ==Examples== | ||
| + | *1.MATRIXTYPE("idempotent",IM(19)) = true | ||
| + | *2.MATRIXTYPE([12,14],"idempotent") = false | ||
| + | *3.MATRIXTYPE(IM(5)|*|2,"idempotent") = false | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/IDENTITY| IDENTITY]] | ||
| + | *[[Manuals/calci/SYMMETRIC| SYMMETRIC]] | ||
| + | *[[Manuals/calci/PASCAL| PASCAL]] | ||
| + | *[[Manuals/calci/TRIANGULAR| TRIANGULAR]] | ||
| + | |||
| + | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Idempotent_matrix Idempotent matrix] | ||
Latest revision as of 08:36, 15 May 2015
MATRIX("IDEMPOTENT",order)
- is the size of the Idempotent matrix.
is the size of the Idempotent matrix.Description
- This function is showing the idempotent matrix of order 3.
- An idempotent matrix is a matrix which, when multiplied by itself, is getting the same matrix.
- i.e.,A square matrix K is said to be idempotent if 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 K^2=K} .
- The properties of idempotent matrix is:
- 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 K^r=K} for r being a positive integer.
- 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 I-K} is idempotent.
- If 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 K_1} 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 K_2} are idempotent matrices 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 K_1K_2 =K_2K_1} . Then 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 K_1K_2} is idempotent.
Examples
- 1.MATRIXTYPE("idempotent",IM(19)) = true
- 2.MATRIXTYPE([12,14],"idempotent") = false
- 3.MATRIXTYPE(IM(5)|*|2,"idempotent") = false