3Blue1Brown
Nonsquare matrices as transformations between dimensions | Essence of linear algebra, chapter 8
How do you think about a non-square matrix as a transformation?
3Blue1Brown
Inverse matrices, column space and null space: Essence of Linear Algebra - Part 7 of 15
How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix?
3Blue1Brown
Inverse matrices, column space and null space | Essence of linear algebra, chapter 6
How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix?
3Blue1Brown
Nonsquare matrices as transformations between dimensions | Essence of linear algebra, footnote
How do you think about a non-square matrix as a transformation?
3Blue1Brown
Nonsquare matrices as transformations between dimensions: Essence of Linear Algebra - Part 8 of 15
How do you think about a non-square matrix as a transformation?
3Blue1Brown
Inverse matrices, column space and null space | Essence of linear algebra, chapter 7
How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix?
Virtually Passed
Least Squares Formula PROOF
First video: https://youtu.be/6eLJSzOHdc8 Linear least squares is a method commonly used to fit curves to data. The equation used for least squares here is derived using the column space of A. The 'best' value of X is the one that...
Curated Video
Data Science and Machine Learning (Theory and Projects) A to Z - Mathematical Foundation: Rank
In this video, we will cover Rank. 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 to Z".In this...
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. 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 to Z".In...
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: Null Space and Column Space Basis
Video first gives examples of finding the column space and null space of a matrix. Shows how to determine if the column space is a basis. Gives an example of finding the basis of the column space if the column space is not already a...
Khan Academy
Khan Academy: Linear Algebra: Showing That the Candidate Basis Does Span C(a)
Video first reviews how to find the basis for the column space of a matrix using the reduced row echelon form. Proves that the basis for the column space using the reduced row echelon form method spans the column space. Uses this and the...
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: Dimension of the Column Space or Rank
Video shows how to find the basis and dimension of the column space by finding its reduced row echelon form and using the columns corresponding to the pivot columns as the basis. Explains that rank is the dimension of the column space....
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: Linear Algebra: Column Space of a Matrix
Video defines the column space as a linear combination of the column vectors and relates it to span. Shows that the column space is a valid subspace. Shows several ways to interpret a column space. This video also appears in the strand...
Khan Academy
Khan Academy: Linear Algebra: Visualizing a Column Space as a Plane in R3
Video reviews how to find a basis for the column space and talks about how to find it more efficiently using reduced row echelon form. Shows a visualization of the column space in R3 as a plane. Shows two methods to determine the...
Khan Academy
Khan Academy: Linear Algebra: Null Space and Column Space Basis
Video first gives examples of finding the column space and null space of a matrix. Shows how to determine if the column space is a basis. Gives an example of finding the basis of the column space if the column space is not already a...
Khan Academy
Khan Academy: Linear Algebra: Null Space and Column Space Basis
Video first gives examples of finding the column space and null space of a matrix. Shows how to determine if the column space is a basis. Gives an example of finding the basis of the column space if the column space is not already a...
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: Linear Algebra: Dimension of the Column Space or Rank
Video shows how to find the basis and dimension of the column space by finding its reduced row echelon form and using the columns corresponding to the pivot columns as the basis. Explains that rank is the dimension of the column space....