@GSMC/이상욱: Principles of Human and Artificial Vision

Lecture 3: Linear Algebra for Computer Vision

maetel 2008. 10. 26. 21:32

eigen value
eigen vector

matrix rank

symmetric matrix
http://en.wikipedia.org/wiki/Symmetric_matrix

eigenvalue decomposition
http://en.wikipedia.org/wiki/Spectral_theorem

singular value decomposition
http://en.wikipedia.org/wiki/Singular_value_decomposition

linear equations
- inhomogeneous equations
- homogeneous equations - unconstrained / constrained



triangular decompostion:
QR, LL, LU decomposition

QR decomposition
http://en.wikipedia.org/wiki/QR_decomposition
- householder transformation
http://en.wikipedia.org/wiki/Householder_transformation
- Givens rotation
http://en.wikipedia.org/wiki/Givens_rotation
- Gram-Schmidt transformation
http://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process

Cholesky LL decomposition
http://en.wikipedia.org/wiki/Cholesky_decomposition

LU decomposition
ref. http://rkb.home.cern.ch/rkb/AN16pp/node160.html#SECTION0001600000000000000000
http://en.wikipedia.org/wiki/LU_decomposition



nonlinear optimization

http://en.wikipedia.org/wiki/Newton%27s_method
http://en.wikipedia.org/wiki/Newton%27s_method_in_optimization

http://en.wikipedia.org/wiki/Linear_least_squares

cf. nonlinear least squares
http://en.wikipedia.org/wiki/Non-linear_least_squares