Difference between revisions of "Manuals/calci/MATRIXTRACE"

Latest revision as of 11:48, 25 April 2019

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.

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

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 *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 \\
@@ Line 16: / Line 16: @@
 ==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==