Khan Academy
Khan Academy: Change of Basis: Alternate Basis Transformation Matrix Part 2
Showing that the transformation matrix with respect to basis B actually works. Brief point on why someone would want to operate in a different basis to begin with.
Khan Academy
Khan Academy: More Determinant Depth: 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.
Khan Academy
Khan Academy: Using Orthogonal Change of Basis Matrix
Video defining an orthogonal matrix as a square matrix C whose columns form an orthonormal set.
Khan Academy
Khan Academy: Changing Coordinate Systems to Help Find a Transformation Matrix
Changing our coordinate system to find the transformation matrix with respect to standard coordinates
Khan Academy
Khan Academy: Change of Basis: Alternate Basis Transformation Matrix Example
Example of finding the transformation matrix for an alternate basis.
Khan Academy
Khan Academy: Transformation Matrix With Respect to a Basis
Finding the transformation matrix with respect to a non-standard basis.
Khan Academy
Khan Academy: Orthogonal Projections: Subspace Projection Matrix Example
This video uses 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.
Khan Academy
Khan Academy: Orthogonal Projections: Another Example of a Projection Matrix
A video lesson figuring out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first.
Khan Academy
Khan Academy: Showing That Inverses Are Linear
Showing that inverse transformations are also linear.
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]