Machine Learning - III. Linear Algebra Review (Week 1, Optional)

机器学习Machine Learning - Andrew NG courses学习笔记

矩阵和向量及其表示介绍

what are matrices矩阵

matrix is just another way for saying, is a 2D or a two dimensional array.
dimension of the matrix is going to be written as the number of row times the number of columns in the matrix.
written out as R4 by 2 or concretely what people will sometimes say this matrix is an element of the set R 4 by 2.
matrix elements,(entries of matrix) the numbers inside the matrix.

the matrix gets you a way of letting you quickly organize, index and access lots of data.

what are vectors向量
A vector turns out to be a special case of a matrix.A vector is a matrix that has only 1 column so you have an N x 1 matrix.{本course中的vector都是列向量}
dimension:if have N equals four elements here.so we also call this is a four dimensional vector, just means that this is a vector with four elements, with four numbers in it.
refer to this as a vector in the set R4.

Notation关于符号的规范表示:

throughout the rest of these videos on linear algebra review, I will be using one index vectors.课程中大多向量下标都是从1开始。
when talking about machine learning applications, sometimes explicitly say when we need to switch to, when we need to use the zero index vectors as well.讨论机器学习应用时会转换到下标从0开始。

Finally, by convention,use upper case to refer to matrices.So we‘re going to use capital letters like A, B, C.and usually we‘ll use lowercase,like a, b, x, y,to refer to either numbers,or just raw numbers or scalars or to vectors.

from: