SFU MATH 232 6.2 Geometry of Linear Operators

SFU Math 232 6.2 Geometry of Linear Operators. Orthogonal transformations, orthogonal matrices, length preservation, the properties of orthogonal matrices and what geometrical they look like - think rotation and reflection.

[haja]

25:00 why are R and the Transpose of R same? That changes the whole result..

[hoaxuan]

The fast Walsh Hadamard transform is an interesting example. Also I like to remind people that the variance equation for linear combinations of random variables applies to dot products.
You can have inside-out artificial neural nets with fixed dot products and adjustable (parametric) activation functions. Obviously you can use fast transforms as systems of fixed dot products.

[hoaxuan]

Sign flipping of a vector. Permutation of a vector. The Walsh Hadamard transform of a vector. Any combination of those.