linear algebra review

Pattern Recognition第一节课ML都不会算了，呵呵，linear algebra忘得一塌糊涂，抓这个周末时间好好好好复习复习咯~

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1. Elementary row operations:

Replacement(Replace one row by the sum of itself and a multiple of another row.)

Interchange(Interchange two rows.)

Scaling(Multiply all entries in a row by a nonzero constant.)

Strictly speaking, in linear algebra, two matrices are row equivalent if one can be changed to the other by a sequence of elementary row operations. 

2. The transpose of a matrix: 将矩阵的行和列换过来

3. Suppose A=[a b; c d], A^-1 A=I   The determinant of A is det A = ad-bc. A is invertible if and only if det A != 0. 行列式符号是在矩阵两边加两个杠。

[A I]  -->  [I A^-1] 

4. The rank of a matrix A, denoted by rank A, is the dimension of the column space of A. A is an invertible matrix if and only if rank A = 0