Math 218: Matrices and Vectors

Welcome! You have found the homepage of the Fall 2024 manifestation of Math 218.

The Four Fundamental Subspaces

To verify if v is in the null space of a matrix A, we can use the syntax A*v == zero_vector(A.nrows()).

To verify if v is in the left null space of a matrix A, we can use the syntax A.T*v == zero_vector(A.ncols()).

To verify if v is in the column space of a matrix A, we can use the syntax A.rank() == A.augment(v).rank().

To verify if v is in the row space of a matrix A, we can use the syntax A.T.rank() == A.T.augment(v).rank().