Manuals/calci/MATRIXRANK

MATRIXRANK (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 rank of the 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 MATRIXRANK(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 order of the matrix.
• The Rank of the matrix is defined by maximum number of columns or Maximum number of rows in the Matrix.
• For 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 rxc} matrix,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 r} is less than 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 c} , then the maximum rank of the matrix 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 r} .
• 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 r} is greater than $c$, then the maximum rank of the matrix 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 c} .
• Suppose all entries are zero in the given matrix then Rank of the Matrix is zero.
• If a matrix had even one non-zero element, its minimum rank would be one.

Examples

1. MATRIXRANK(IM(9)) = 9
2. MATRIXRANK([[2,5,8,9],[3,4,6,1],[9,6,5,2]]) = 3
3. MATRIXRANK([[2,5],[8,9],[3,4],[6,1],[9,6],[5,2]]) = 2

Related Videos

Dimension of Column

See Also

• MATRIXOPERATIONS
• TRANSPOSE
• MDETERM

References

• Matrix rank

• List of Main Z Functions
• Z3 home