Matrix class preparation on Decomposition--(1)

特征值正交分解 A=PDP', where P'=inverse(P), D is diagonal matrix of eigenvalues.特点： A^{n} = PD^{n}P';  e^{A}=Pe^{D}P'

QR分解 A=QR, where R is an upper triangular matrix and Q is an orthogonal matrix. QR 分解常用于解线性方程组。

LU分解 A=LU, where L is an lower triangular matrix and U an  upper triangular matrix . QR 分解常用于解Ax=b=>L(Ux)=b=>Ly=b, Ux=y。

SVD分解 A=UDV', where A is m-n matrix, and D is n-n diagonal matrix.  U is m-n matrix and V is n-n matrix such that U'U=V'V=I. 不是所有的矩阵都可以特征值分解，但是所有的实矩阵都可以特征值分解。

SVD一个用途是二次误差最佳逼近。这个含义上SVD, PCA, Fourier很像。
在mutiview里面，SVD几乎是处理fundmental matrix的必用工具。

further reading:

• Direct Least Squares Fitting of Ellipses by Fitzgibbon
• http://www.uwlax.edu/faculty/will/svd/index.html
• Invariant Subspaces and Condition  and Singular Value Decomposition
• A few properties of Singular Value Decomposition