Instructional Video9:40
Professor Dave Explains

Further Matrix Decompositions: LU, Cholesky, QR, and SVD

9th - Higher Ed
We've learned about matrix diagonalization, which is a type of matrix decomposition. There are some others that we must learn, including LU decomposition, Cholesky decomposition, QR decomposition, and singular value decomposition. Let's...
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Visualizations of Left Nullspace and Rowspace

9th - 10th
Video builds upon the column spaces and null spaces of the 2x3 matrix and its transpose found in the previous video. Uses them to explain some relationships between the four fundamental subspaces, namely that the orthogonal complement of...
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Rowspace and Left Nullspace

9th - 10th
Video reviewing two fundamental subspaces of a matrix (null space and column space) and introducing two more (row space and left null space). Finds each of these subspaces for a specific 2x3 matrix and its transpose. Demonstrates that...
Instructional Video
Khan Academy

Khan Academy: Linear Algebra: Orthogonal Complements as Subspaces

9th - 10th
Video introducing the orthogonal complement of a subspace and showing that it is also a subspace. Proves that the null space of a matrix is equivalent to the orthogonal complement of its row space by showing that every member of the null...
Instructional Video
Khan Academy

Khan Academy: Orthogonal Complements: Orthogonal Complement of the Nullspace

9th - 10th
A video lesson illustrating that the orthogonal complement of the nullspace is equal to the row space and vice versa.