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Professor Dave Explains
Further Matrix Decompositions: LU, Cholesky, QR, and SVD
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...
Curated Video
Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: Eigen Space
In this video, we will cover Eigen Space.
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning (Theory and Projects) A...
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This clip is from the chapter "Machine Learning: Feature Engineering and Dimensionality Reduction with Python" of the series "Data Science and Machine Learning (Theory and Projects) A...
Zach Star
Dear linear algebra students, This is what matrices (and matrix manipulation) really look like
Dear linear algebra students, This is what matrices (and matrix manipulation) really look like
Khan Academy
Khan Academy: Linear Algebra: Unique Row Space Solution to Ax = B
A video lesson proving that there is a unique solution in the row space of A to the equation Ax = b, where A is some m x n matrix, b is a vector that is a particular member of the column space of A, and x is a member of Rn. The solution...
Khan Academy
Khan Academy: Linear Algebra: Visualizations of Left Nullspace and Rowspace
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...
Khan Academy
Khan Academy: Linear Algebra: Rowspace and Left Nullspace
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...
Khan Academy
Khan Academy: Linear Algebra: Row Space Solution to Ax = B Example
An instructional video that gives an example of how to find a solution to the equation Ax = b. In the example, the matrix A is 2 x 2. Shows that when the solution is a member of the row space of A for a given vector b, a member of the...
Khan Academy
Khan Academy: Linear Algebra: Orthogonal Complements as Subspaces
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...
Khan Academy
Khan Academy: Orthogonal Complements: Unique Rowspace Solution to Ax=b
This video shows that, for any b that is in the column space of A, there is a unique member of the row space that is the "smallest" solution to Ax=b.
Khan Academy
Khan Academy: Orthogonal Complements: Orthogonal Complement of the Nullspace
A video lesson illustrating that the orthogonal complement of the nullspace is equal to the row space and vice versa.
Khan Academy
Khan Academy: Linear Algebra: Row Space Solution to Ax = B Example
An instructional video that gives an example of how to find a solution to the equation Ax = b. In the example, the matrix A is 2 x 2. Shows that when the solution is a member of the row space of A for a given vector b, a member of the...
Khan Academy
Khan Academy: Orthogonal Complements: Orthogonal Complements
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...