Alternate coordinate systems (bases) | Linear Algebra | Khan Academy (English)

   Tuesday, July 13, 2021   

Starting a new Lecture Notes Series on Alternate coordinate systems (bases) | Linear Algebra | Khan Academy

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Alternate coordinate systems (bases) | Linear Algebra | Khan Academy
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Lecture Description of this above Topic:

Lecture 1: Eigenvalues of a 3x3 matrix

Lecture 2: Change of basis matrix

Lecture 3: Finding eigenvectors and eigenspaces example

Lecture 4: Eigenvectors and eigenspaces for a 3x3 matrix

Lecture 5: Projections onto subspaces

Lecture 6: Introduction to orthonormal bases

Lecture 7: Least squares examples | Alternate coordinate systems (bases)

Lecture 8: Showing that an eigenbasis makes for good coordinate systems

Lecture 9: Alternate basis transformation matrix example part 2

Lecture 10: Changing coordinate systems to help find a transformation matrix

Lecture 11: Orthogonal complement of the nullspace

Lecture 12: Representing vectors in rn using subspace members

Lecture 13: Least squares approximation

Lecture 14: Introduction to eigenvalues and eigenvectors

Lecture 15: Transformation matrix with respect to a basis

Lecture 16: Orthogonal complements

Lecture 17: Subspace projection matrix example

Lecture 18: Another least squares example

Lecture 19: Finding projection onto subspace with orthonormal basis example

Lecture 20: Coordinates with respect to orthonormal bases

Lecture 21: Another example of a projection matrix

Lecture 22: Gram-Schmidt example with 3 basis vectors

Lecture 23: Projection is closest vector in subspace

Lecture 24: A projection onto a subspace is a linear transformation

Lecture 25: Unique rowspace solution to Ax = b

Lecture 26: Example using orthogonal change-of-basis matrix to find transformation matrix

Lecture 27: Alternate basis transformation matrix example

Lecture 28: Invertible change of basis matrix

Lecture 29: dim(v) + dim(orthogonal complement of v) = n

Lecture 30: Example solving for the eigenvalues of a 2x2 matrix

Lecture 31: Rowspace solution to Ax = b example

Lecture 32: The Gram-Schmidt process

Lecture 33: Proof of formula for determining eigenvalues

Lecture 34: Gram-Schmidt process example

Lecture 35: Visualizing a projection onto a plane

Lecture 36: Coordinates with respect to a basis

Lecture 37: Projections onto subspaces with orthonormal bases

Lecture 38: Orthogonal matrices preserve angles and lengths

Lecture 39: Orthogonal complement of the orthogonal complement