Manuals/calci/MATRIXTRACE

MATRIXTRACE (a)

• $a$ is any matrix.

Description

• 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.

Examples

1. MATRIXTRACE([[5,19,-36,10,7.6],[20,-17,4.5,43,87]]) = -12
2. MATRIXTRACE([[10,18,-76,-98],[12,85.4,65,78],[10,15,76,123]]) = 171.4
3. 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

Trace Matrix

See Also

• MATRIXMULTIPLY
• MATRIXOPERATORS
• MATRIXMOD

References

• Trace

• List of Main Z Functions
• Z3 home