# MatrixManipulation(R, Row, Col, M)ΒΆ

- R: Type
- Row: FiniteLinearAggregate R
- Col: FiniteLinearAggregate R
- M: TwoDimensionalArrayCategory(R, Row, Col)

Some functions for manipulating (dense) matrices. Supported are various kinds of slicing, splitting and stacking of matrices. The functions resemble operations often used in numerical linear algebra algorithms.

- bandMatrix: (M, List Integer) -> M if R has AbelianMonoid
`bandMatrix`

returns multiple diagonals out of a matrix. The diagonals are put into a matrix of same shape as the original one. Positive integer arguments select upper off-diagonals, negative ones lower off-diagonals.

- bandMatrix: (M, Segment Integer) -> M if R has AbelianMonoid
`bandMatrix`

returns multiple diagonals out of a matrix. The diagonals are put into a matrix of same shape as the original one. Positive integer arguments select upper off-diagonals, negative ones lower off-diagonals.

- blockSplit: (M, List NonNegativeInteger, PositiveInteger) -> List List M
`blockSplit`

splits a matrix into multiple submatrices row and column wise, dividing a matrix into blocks.

- blockSplit: (M, PositiveInteger, List NonNegativeInteger) -> List List M
`blockSplit`

splits a matrix into multiple submatrices row and column wise, dividing a matrix into blocks.

- columnMatrix: (M, Integer) -> M
`columnMatrix`

returns a single column out of a matrix. The column is put into a one by`N`

matrix.

- columns: (M, List Integer) -> M
`columns`

returns several columns out of a matrix. The columns are stacked into a matrix.

- columns: (M, Segment Integer) -> M
`columns`

returns several columns out of a matrix. The columns are stacked into a matrix.

- diagonalMatrix: (M, Integer) -> M if R has AbelianMonoid
`diagonalMatrix`

returns a diagonal out of a matrix. The diagonal is put into a matrix of same shape as the original one. Positive integer arguments select upper off-diagonals, negative ones lower off-diagonals.

- diagonalMatrix: M -> M if R has AbelianMonoid
`diagonalMatrix`

returns the main diagonal out of a matrix. The diagonal is put into a matrix of same shape as the original one.

- element: (M, Integer, Integer) -> M
`element`

returns a single element out of a matrix. The element is put into a one by one matrix.

- rowMatrix: (M, Integer) -> M
`rowMatrix`

returns a single row out of a matrix. The row is put into a one by`N`

matrix.

- rows: (M, List Integer) -> M
`rows`

returns several rows out of a matrix. The rows are stacked into a matrix.

- rows: (M, Segment Integer) -> M
`rows`

returns several rows out of a matrix. The rows are stacked into a matrix.