3Blue1Brown
Change of basis: Essence of Linear Algebra - Part 13 of 15
What is a change of basis, and how do you do it?
3Blue1Brown
Change of basis | Essence of linear algebra, chapter 13
What is a change of basis, and how do you do it?
3Blue1Brown
Change of basis | Essence of linear algebra, chapter 9
What is a change of basis, and how do you do it?
Curated Video
Create a computer vision system using decision tree algorithms to solve a real-world problem : Image Transformations – Perspective transform
From the section: Computer Vision Basics: Part 2. In this section, we’ll explore the some addtiional features of Computer Vision. Computer Vision Basics: Part 2: Image Transformations – Perspective transform
Curated Video
Create a computer vision system using decision tree algorithms to solve a real-world problem : [Activity] Perform non-affine image transformation on a traffic sign image
From the section: Computer Vision Basics: Part 2. In this section, we’ll explore the some addtiional features of Computer Vision. Computer Vision Basics: Part 2: [Activity] Perform non-affine image transformation on a traffic sign image
Khan Academy
Khan Academy: Linear Algebra: Deriving a Method for Determining Inverses
An instructional video that explains how the method for finding the inverse transformation matrix is derived. It is the same method for finding the inverse for any invertible matrix. [18:00]
Khan Academy
Khan Academy: Linear Algebra: Compositions of Linear Transformations 2
Video shows that the transformation matrix of the composition of linear functions is the product of the transformation matrices of each linear transformation in the composition. [16:30]
Khan Academy
Khan Academy: Linear Algebra: Why Eigenbases Make for Good Coordinate Systems
Video creating a basis out of n linearly independent eigenvectors. Reviews transformations and change of basis matrices. Shows that when the eigenbasis is used as an alternate coordinate system, the transformation is a diagonal matrix...
Khan Academy
Khan Academy: Linear Algebra: Alternate Basis Transformation Matrix Example Pt 2
Video continuing the example from the previous video where a transformation matrix with respect to an alternate basis was found given a transformation matrix with respect to the standard basis, an alternate basis and a change of basis...
Khan Academy
Khan Academy: Linear Algebra: Determinant as Scaling Factor
Video demonstrating that the area of a parallelogram that is the image of a rectangle under a transformation is equivalent to the absolute value of the determinant of the matrix whose column vectors generate the parallelogram. Includes...
Khan Academy
Khan Academy: Linear Algebra: Using Orthogonal Change of Basis Matrix Example
Video defining an orthogonal matrix as a square matrix C whose columns form an orthonormal set. Shows that C will be invertible and that multiplying C transpose by C will result in the identity matrix. The result that C transpose equals...
Khan Academy
Khan Academy: Linear Algebra: Expressing Projection as Matrix Vector Product
Video shows how to simplify the vector projection formula using unit vectors. Shows that projections are linear transformations. Shows the general formula for the transformation matrix for projections in R^2. Shows an example using the...
Khan Academy
Khan Academy: Linear Algebra: Expressing Projection as Matrix Vector Product
Video shows how to simplify the vector projection formula using unit vectors. Shows that projections are linear transformations. Shows the general formula for the transformation matrix for projections in R^2. Shows an example using the...
Khan Academy
Khan Academy: Linear Algebra: Change Bases to Help Find a Transformation Matrix
Video showing how to change coordinate systems to make finding the transformation matrix with respect to the standard basis easier. First, a specific linear transformation is defined and the regular method for constructing the...
Khan Academy
Khan Academy: Linear Algebra: Alternate Basis Transformation Matrix Example
Video reviewing the relationship between transformation matrices with respect to different bases. Addresses manipulating the equation to write it in terms of the transformation matrix with respect to the standard basis. The relationship...
Khan Academy
Khan Academy: Linear Algebra: Linear Transformation Examples: Rotations in R2
Video first shows visually that a rotation is a linear transformation. Shows how to construct a transformation matrix that will rotate a vector through a given angle. Shows both the general rotation matrix and an example of a rotation...
Khan Academy
Khan Academy: Linear Algebra: Showing That Inverses Are Linear
A video lesson that gives an in-depth, algebraic proof showing that the inverse of a linear transformation is also linear. [21:25]
Khan Academy
Khan Academy: Linear Algebra: Transformation Matrix With Respect to a Basis
Video discussing transformation matrices and how a vector is able to be mapped to the same resulting vector by using a transformation matrix with respect to the standard basis as well as one with respect to a different basis. Reviews how...
Khan Academy
Khan Academy: Linear Algebra: Subpsace Projection Matrix Example
An instructional video that works through a concrete example for how to find the projection of an arbitrary vector onto a specific subspace in R4. Uses a 4 x 2 basis matrix for the subspace. Matrix operations are used along with the...
Khan Academy
Khan Academy: Linear Algebra: Another Example of a Projection Matrix
A video lesson working another example for finding the projection of an arbitrary vector onto a specific subspace in R3. The basis of the subspace is a 3 x 2 matrix. Uses an alternate method for find the transformation matrix that...
Khan Academy
Khan Academy: Linear Algebra: Rotation in R3 Around the X Axis
Video shows how to write a transformation matrix in R^3 that rotates a vector around the x-axis. Compares the rotation matrix in R^3 to the rotation matrix in R^2 found in the previous video and discusses how it could be applied for more...
Khan Academy
Khan Academy: Linear Algebra: Linear Transformations: Scaling and Reflections
Video first reviews how to find the transformation matrix using the identity matrix. Shows how to write a transformation matrix that reflects over the y-axis and scales the y-coordinates by a factor of 2. [15:13]
Khan Academy
Khan Academy: Linear Algebra: Compositions of Linear Transformations 2
Video shows that the transformation matrix of the composition of linear functions is the product of the transformation matrices of each linear transformation in the composition. [16:30]
Khan Academy
Khan Academy: Showing That an Eigenbasis Makes for Good Coordinate Systems
Video creating a basis out of n linearly independent eigenvectors. Reviews transformations and change of basis matrices. Shows that when the eigenbasis is used as an alternate coordinate system, the transformation is a diagonal matrix...