Linear algebra MOC

Row and column space

The column space of a matrix is the span of its columns, linalg or considered as a Linear map, the target Vector subspace. Hence it is sometimes referred to as the range or the image of a matrix.

Dually, the row space of a matrix is the span of its rows. linalg It is therefore the range of linear functionals made by premultiplying the matrix by a linear functional.

Basis

A basis for a row space can be performed by performing Gaußian elimination on the matrix , since all non-zero rows of a matrix in Row echelon form are independent.

Likewise, the basis of a column space of a matrix is found by performing gaussian elimination on the transpose , and then transposing the results back to column vectors.

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