Manuals/calci/TRACE

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. TRACE([3,6,9;12,-67,-98;45,23,98]) = 34
2. TRACE([[10,15,-19,43.2],[78,56,-90,32.9],[1,17,-143,187],[15,18,432,987]]) = 910
3. TRACE([[3,8],[10,12]]) = 15

See Also

• MATRIXMULTIPLY
• MATRIXOPERATORS
• MATRIXMOD

References

• Trace

• List of Main Z Functions
• Z3 home