Manuals/calci/MATRIXTYPE

MATRIXTYPE (Matrix,Type)

• $Matrix$ is the set of values.
• $Type$ is the type of the matrix.

Description

• This function is the tester function of Idempotent and Projection matrix.
• In $MATRIXTYPE(Matrix,Type)$,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 Matrix} is set of values 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 Type} is the type of the matrix either Idempotent or Projection.
• Idempotent a matrix which, when multiplied by itself, yields itself.
• A square matrix P is called Projection then 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 P^2=P} .
• So the given matrix values are satisfied Idempotent and the given Matrix Type also Idempotent then this function will return as TRUE otherwise FALSE.
• In same way the given values are satisfies Projection and the Matrix Type also Projection then this function will return as TRUE otherwise FALSE.

Examples

1. MATRIXTYPE(IM(2),"idempotent") = true
2. MATRIXTYPE([[1,0,1],[0,1,2]],"idempotent") = false
3. MATRIXTYPE([[1,0,0],[0,1,0],[0,0,1]],"projection") = true
4. MATRIXTYPE([[1,0,1],[0,1,0],[0,0,1]],"projection") = false

Related Videos

Types of a Matrix

See Also

• MATRIXIDENTITY
• MATRIXOPERATORS

References

• Identity

• List of Main Z Functions
• Z3 home