Manuals/calci/MATRIXTRACE
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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 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