Difference between revisions of "Manuals/calci/MATRIXTRACE"

Revision as of 16:29, 5 July 2017

MATRIXTRACE (a)

This function shows the trace value of the given matrix.
In $MATRIXTRACE(a)$ , $a$ 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 $(a_{ij})$ .
Here trace of the matrix A is $tr(A)=a_{11}+a_{22}+...a_{nn}$ = $\sum _{i=1}^{n}a_{ii}$ .Where $a_{ii}$ denotes the entry on the $ith$ row and $ith$ column of A.
Now consider 3x3 matrix $A={\begin{pmatrix}a&b&c\\d&e&f\\g&h&i\end{pmatrix}}$
Here tr(A)= a+e+j.

@@ Line 7: / Line 7: @@
 *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.
+*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 \\