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

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

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

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

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

6. Example M = U S V^T

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

8. 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

9. References Wikipedia. Singular Value Decomposition. Retrieved from: http://zh.wikipedia.org/wiki/singularvaluedecomposition / http://zh.wikipedia.org/wiki/singularvaluedecomposition / China Math Research Center(Dec 09, 2014). Specific Math. Examples for SVD. Retrieved from: http://wenku.baidu.com/link?url=UjxpIJ7B2EypDxrkBw8dkim81MqC_FSUCxQUzh8jkJU6JgGaIUAyjcB9w cQIC43g1KbMcQn5zC8dOCj8jSORiaZnGB4Wu0dUlEPIDLlL5vq http://wenku.baidu.com/link?url=UjxpIJ7B2EypDxrkBw8dkim81MqC_FSUCxQUzh8jkJU6JgGaIUAyjcB9w cQIC43g1KbMcQn5zC8dOCj8jSORiaZnGB4Wu0dUlEPIDLlL5vq Machine Learning(Nov 18, 2014). Singular Value Decomposition. Retrieved from: http://v.163.com/movie/2008/1/J/V/M6SGF6VB4_M6SGKINJV.html

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