Manuals/calci/IDEMPOTENT

MATRIX("IDEMPOTENT",order)

• $order$ is the size of the Idempotent matrix.

Description

• This function is showing the idempotent matrix of order 3.
• An idempotent matrix is a matrix which, when multiplied by itself, is getting the same matrix.
• i.e.,A square matrix K is said to be idempotent if 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 K^2=K} .
• The properties of idempotent matrix is:

1. 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 K^r=K} for r being a positive integer.
2. 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 I-K} is idempotent.
3. If 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 K_1} 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 K_2} are idempotent matrices and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle K_{1}K_{2}=K_{2}K_{1}} . 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 K_1K_2} is idempotent.

Examples

• 1.MATRIXTYPE("idempotent",IM(19)) = true
• 2.MATRIXTYPE([12,14],"idempotent") = false
• 3.MATRIXTYPE(IM(5)|*|2,"idempotent") = false

See Also

• IDENTITY
• SYMMETRIC
• PASCAL
• TRIANGULAR

References

• Idempotent matrix