Euclidean Subspace - Algorithms

Algorithms

Most algorithms for dealing with subspaces involve row reduction. This is the process of applying elementary row operations to a matrix until it reaches either row echelon form or reduced row echelon form. Row reduction has the following important properties:

1. The reduced matrix has the same null space as the original.
2. Row reduction does not change the span of the row vectors, i.e. the reduced matrix has the same row space as the original.
3. Row reduction does not affect the linear dependence of the column vectors.