SVD ？ name ： Bei Wang COM471 Algorithms and Mathematics for Games and Graphics 19/03/2015.

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Presentation transcript:

SVD ？ name ： Bei Wang COM471 Algorithms and Mathematics for Games and Graphics 19/03/2015

1.Definition 2.Python & Math 3.Examples 4.Invert matrix Outline

Definition SVD = Singular Value Decomposition A way to split a matrix into 3 parts

Python U,S,Vt = numpy.linalg.svd(M)

Math M=U*S*V^T Rotation matrix diagonal scaling matrix SVD is a rotate-scale-rotate pattern

Example M = U S V^T

Example M = M = USV^T UU^T= S = V^T= U = VV^T=

Invert Matrix  The inverse of a rotation matrix is just the Transpose of that matrix  The inverse of a diagonal matrix is just the reciprocal of the elements on the diagonal  Inverse of M is V*(1/S)*U^T

References Wikipedia. Singular Value Decomposition. Retrieved from: / / China Math Research Center(Dec 09, 2014). Specific Math. Examples for SVD. Retrieved from: cQIC43g1KbMcQn5zC8dOCj8jSORiaZnGB4Wu0dUlEPIDLlL5vq cQIC43g1KbMcQn5zC8dOCj8jSORiaZnGB4Wu0dUlEPIDLlL5vq Machine Learning(Nov 18, 2014). Singular Value Decomposition. Retrieved from:

Q & A name ： Bei Wang COM471 Algorithms and Mathematics for Games and Graphics 17/03/2015