矩阵运算中的一些有趣的关系

一些关系：

Sum of eigvalues of A equals the trace of (A);
Show that f(Xn×n) = trace (X) is a linear function. from matrix_analysis.pdf
For matrices Am×n and Bn×m, prove that trace (AB) = trace (BA). from matrix_analysis.pdf

2-gi07.pdf（GI07/COMPM012: Mathematical Programming and Research Methods (Part 2)） 中的(I − QQ>和
数值分析第5章.ppt 定理20 如果||B||<1，则I+B非奇异矩阵，

PCA和Least Squares Regression 有关系。参考Thesis_def.pdf

Least Squares, QR and SVD的关系：lecture09.pdf

good summary of svd: lecture6.pdf