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Videos from “khanacademy” (25 video results)
Showing that an eigenbasis makes for good coordinate systems
Eigenvectors and eigenspaces for a 3x3 matrix
Determining the eigenvalues of a 3x3 matrix
Finding the eigenvectors and eigenspaces of a 2x2 matrix
Example solving for the eigenvalues of a 2x2 matrix
Proof of formula for determining Eigenvalues
What eigenvectors and eigenvalues are and why they are interesting
Gram-Schmidt example with 3 basis vectors
Using Gram-Schmidt to find an orthonormal basis for a plane in R3
Finding an orthonormal basis for a subspace using the Gram-Schmidt Process
Showing that orthogonal matrices preserve angles and lengths
Example using orthogonal change-of-basis matrix to find transformation matrix
Example of finding the transformation matrix for the projection onto a subspace with an orthonormal basis
Projections onto subspaces with orthonormal bases
Seeing that orthonormal bases make for good coordinate systems
Looking at sets and bases that are orthonormal -- or where all the vectors have length 1 and are orthogonal to each other.
Changing our coordinate system to find the transformation matrix with respect to standard coordinates
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.
Example of finding the transformation matrix for an alternate basis
Finding the transformation matrix with respect to a non-standard basis
Using an invertible change of basis matrix to go between different coordinate systems
Using a change of basis matrix to get us from one coordinate system to another.
Understanding alternate coordinate systems
An example using the least squares solution to an unsolvable system
Using least squares approximation to fit a line to points
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