Difference between revisions of "Manuals/calci/MATRIXTRACE"
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(Created page with "<div style="font-size:30px">'''MATRIXTRACE (a) '''</div><br/> *<math> a </math> is any matrix. ==Description== *This function shows the trace value of the given matrix. *In <...") |
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*The trace of an nxn square matrix is defined to be the sum of all main diagonal entries. | *The trace of an nxn square matrix is defined to be the sum of all main diagonal entries. | ||
*Consider the matrix A with the elements <math>(a_{ij})</math>. | *Consider the matrix A with the elements <math>(a_{ij})</math>. | ||
| − | *Here trace of the matrix A is <math>tr(A)=a_{11}+a_{22}+...a_{nn}</math>=<math>sum_{i=1}^n a_{ii}</math>.Where <math>a_{ii}</math> denotes the entry on the <math>ith</math> row and <math>ith</math> column of A. | + | *Here trace of the matrix A is <math>tr(A)=a_{11}+a_{22}+...a_{nn}</math>=<math>\sum_{i=1}^n a_{ii}</math>.Where <math>a_{ii}</math> denotes the entry on the <math>ith</math> row and <math>ith</math> column of A. |
*Now consider 3x3 matrix <math> A=\begin{pmatrix} | *Now consider 3x3 matrix <math> A=\begin{pmatrix} | ||
a & b &c \\ | a & b &c \\ | ||
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==Examples== | ==Examples== | ||
| + | # MATRIXTRACE([[5,19,-36,10,7.6],[20,-17,4.5,43,87]]) = -12 | ||
| + | # MATRIXTRACE([[10,18,-76,-98],[12,85.4,65,78],[10,15,76,123]]) = 171.4 | ||
| + | # MATRIXTRACE([[21,54,98,10,17,23],[90,87,65,43,12,10],[13,-543,-987,-154,100,32],[67,87,97,32,11,987]]) = -847 | ||
| + | |||
| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|v=3AjxKor5OiQ|280|center|Trace Matrix}} | ||
==See Also== | ==See Also== | ||
Latest revision as of 11:48, 25 April 2019
MATRIXTRACE (a)
- is any matrix.
is any matrix.Description
- This function shows the trace value of the given matrix.
- 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 MATRIXTRACE (a)} , 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} is any matirx.
- The trace of an nxn square matrix is defined to be the sum of all main diagonal entries.
- Consider the matrix A with the elements 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_{ij})} .
- Here trace of the matrix A 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 tr(A)=a_{11}+a_{22}+...a_{nn}} =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 \sum_{i=1}^n a_{ii}} .Where 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_{ii}} denotes the entry on the 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 ith} row 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 ith} column of A.
- Now consider 3x3 matrix 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=\begin{pmatrix} a & b &c \\ d & e &f \\ g &h & i \end{pmatrix} }
- Here tr(A)= a+e+j.
Examples
- MATRIXTRACE([[5,19,-36,10,7.6],[20,-17,4.5,43,87]]) = -12
- MATRIXTRACE([[10,18,-76,-98],[12,85.4,65,78],[10,15,76,123]]) = 171.4
- MATRIXTRACE([[21,54,98,10,17,23],[90,87,65,43,12,10],[13,-543,-987,-154,100,32],[67,87,97,32,11,987]]) = -847