Manuals/calci/TRACE

MATRIXTRACE (a)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a } is any matrix.

Description

• This function shows the trace value of the given matrix.
• In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle MATRIXTRACE (a)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle tr(A)=a_{11}+a_{22}+...a_{nn}} =Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_{i=1}^n a_{ii}} .Where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_{ii}} denotes the entry on the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ith} row and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ith} column of A.
• Now consider 3x3 matrix Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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