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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 <..."
<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 <math>MATRIXTRACE (a)</math>, <math>a</math> 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 <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.
*Now consider 3x3 matrix <math> A=\begin{pmatrix}
a & b &c \\
d & e &f \\
g &h & i
\end{pmatrix} </math>
*Here tr(A)= a+e+j.
==Examples==
==See Also==
*[[Manuals/calci/MATRIXMULTIPLY| MATRIXMULTIPLY]]
*[[Manuals/calci/MATRIXOPERATORS| MATRIXOPERATORS]]
*[[Manuals/calci/MATRIXMOD| MATRIXMOD ]]
==References==
*[https://en.wikipedia.org/wiki/Trace_(linear_algebra) Trace]
*[[Z_API_Functions | List of Main Z Functions]]
*[[ Z3 | Z3 home ]]
*<math> a </math> is any matrix.
==Description==
*This function shows the trace value of the given matrix.
*In <math>MATRIXTRACE (a)</math>, <math>a</math> 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 <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.
*Now consider 3x3 matrix <math> A=\begin{pmatrix}
a & b &c \\
d & e &f \\
g &h & i
\end{pmatrix} </math>
*Here tr(A)= a+e+j.
==Examples==
==See Also==
*[[Manuals/calci/MATRIXMULTIPLY| MATRIXMULTIPLY]]
*[[Manuals/calci/MATRIXOPERATORS| MATRIXOPERATORS]]
*[[Manuals/calci/MATRIXMOD| MATRIXMOD ]]
==References==
*[https://en.wikipedia.org/wiki/Trace_(linear_algebra) Trace]
*[[Z_API_Functions | List of Main Z Functions]]
*[[ Z3 | Z3 home ]]