Vector Spaces Associated with a Matrix

There are four vector spaces naturally associated with an m×n matrix A: the row space, the column space, and the left and right nullspaces. A basis for a vector space is a linearly independent set of vectors that spans the space.

• The Row Space
• The Column Space
• The Left and Right Nullspaces
• The QR Factorization and Orthonormal Bases
• Rank and Dimension
• Related topics