Difference between revisions of "JordanDiagonalization Command"
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| − | <noinclude>{{Manual Page|version=5.0}}{{command|cas=true|JordanDiagonalization}}</noinclude> | + | <noinclude>{{Manual Page|version=5.0}}{{command|cas=true|US_version=JordanDiagonalization|non-US_version=JordanDiagonalisation}}</noinclude> |
==CAS Syntax== | ==CAS Syntax== | ||
;JordanDiagonalization( <Matrix> ) | ;JordanDiagonalization( <Matrix> ) | ||
| − | :Decomposes the given matrix into the form | + | :Decomposes the given matrix into the form S J S⁻¹ where J is in [http://mathworld.wolfram.com/JordanCanonicalForm.html Jordan Canonical Form] |
| − | :{{example|1=<code><nowiki>JordanDiagonalization({{1, 2}, {3, 4}})</nowiki></code> yields <math> | + | :{{example|1=<code><nowiki>JordanDiagonalization({{1, 2}, {3, 4}})</nowiki></code> yields <math> \left(\begin{array}{}\sqrt{33} - 3&-\sqrt{33} - 3\\6&6\\\end{array}\right) </math>, <math> \left(\begin{array}{}\frac{\sqrt{33} + 5}{2}&0\\0&\frac{-\sqrt{33} + 5}{2}\\\end{array}\right) </math> }} |
{{note| 1=<div> | {{note| 1=<div> | ||
| − | * See also [[Eigenvalues Command]], [[Eigenvectors Command]] | + | * See also [[Eigenvalues Command]], [[Eigenvectors Command]], [[SVD Command]], [[Invert Command]], [[Transpose Command]] |
</div>}} | </div>}} | ||
Revision as of 15:06, 26 June 2018
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This command differs among variants of English:
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CAS Syntax
- JordanDiagonalization( <Matrix> )
- Decomposes the given matrix into the form S J S⁻¹ where J is in Jordan Canonical Form
- Example:
JordanDiagonalization({{1, 2}, {3, 4}})yields \left(\begin{array}{}\sqrt{33} - 3&-\sqrt{33} - 3\\6&6\\\end{array}\right) , \left(\begin{array}{}\frac{\sqrt{33} + 5}{2}&0\\0&\frac{-\sqrt{33} + 5}{2}\\\end{array}\right)
Note:
