斯坦福大学ML(3)——线性代数回顾(Linear Algebra Review)

3 - 1 - Matrices and Vectors 

       （向量是n行*1列的矩阵）Vecot: An n*1 matrix.（在数学中下标从1开始比较多，在机器学习中下标从0开始比较多）

3 - 4 - Matrix Matrix Multiplication 

       （在高度优化下，做到矩阵矩阵相乘高效的乘法）highly optimized in order to do that, matrix matrix multiplication very efficiently, （包括采取一些优化处理方式如并行计算）including taking a advantage of any parallel computation that your computer may be  capable
of,（当你电脑有多个调度或者多个处理器）when your computer has multiple calls or lots of multiple processors, （一个处理器有时存在并行计算，我们称之为SIMD并行）within a processor sometimes there's parallelism as well called symdiparallelism [sp].（在计算机管理机制下，你将会有非常不错的免费类库来高效计算矩阵矩阵相乘）The
computer take care of and you should take a lot of very good free libraries that you can to do this matrix matrix multiplication very efficiently so that you knows,（方便计算有很多假设集的预测数据） makes lots of predictions of lots of hypotheses.

       （矩阵是非常有用，因为你可以通过矩阵乘法将大量运算打包到一次矩阵的乘法运算中）Matrix multiplication is really useful since you can pack a lot of computation into just one matrix multiplication operation.（A*B不等于B*A）It's not commutative.（矩阵运算服从结合律）multiplication
can enjoy the associative property.



3 - 6 - Inverse and Transpose 

       （转置：将行转为列，列转为行）if B = A(T), so B_ij = A_ji