心血来潮,写点儿有关线性代数的知识点和自己的理解,希望对自己的期末复习有用 Vector Spaces 向量空间 设V是个非空集合,F是一个域。 addition:两个向量x,y它们的和 x+y 仍在空间V内 scalar multiplication:对…
(Remark:The letterFis used becauseRandCare examples of what are calledfields) Elements ofFare called scalars.The words "scalar",a fancy word for "number",is often used when we want to emphasize that an object is a number,as opposed to a vector(vectors will be difined soon). Forα∈Fand...
A vector u is called a unit vector if the norm of u is 1, or, equivalently, if u\dot u=1. Theorem 1.3 Cauchy-Schwarz inequality Throrem 1.4 39:57 Distance 42:12 angle 45:58 projection Chapter 2 Algebra of Matrices For a single element a_{ij}, i shows which row the element is ...
The reader will undoubtedly have met most of the concepts in connection with vectors in ordinary three-dimensional space and probably also in a standard first course on linear algebra and matrices. To many, therefore, this chapter will be revision, but it should not be treated too lightly ...
第四节:Vector Spaces An indexed set {v1, v2, ... ... vp} of two or more vectors, with vi != 0, is linearly dependent, if and only if some vj (with j > 1) is a linear combination of the preceding vectors. Elementary row operation on a matrix do not affect the linear depende...
Vector Spaces and Subspaces: https://math.mit.edu/~gs/dela/dela_5-1.pdf https://web.mit.edu/18.06/www/:18.06 Linear Algebra@MIT https://math.mit.edu/~gs/:Gilbert Strang Linear Algebra and Vector Analysis: https://people.math.harvard.edu/; Math 22b Spring 2019:https://people.math....
Chapter 4 Vector Spaces Theorems If v1, ... ,vp are in a vector space V, then Span{v1, ... ,vp} is a subspace of V. 张成集性质,说明张成集是一个子空间。向量空间的一些向量的张成集必定是这个向量空间的子集。 The null space of an m*n matrix A is a subspace of Rn. Equivalently...
Linear Algebra (chapter4)01
LectureNoteonLinearAlgebra 13.VectorSpacesandSubspaces Wei-ShiZheng, wszheng@ieee,2011 October29,2011 1WhatDoYouLearnfromThisNote Example:Define⃗x=−1 2 3,⃗y=4 0 6,⃗z=7 8 −9.Pleaseverify: (1)⃗x+⃗y=⃗y+⃗x;...
vector Elements of a vector space are calledvectorsorpoints. The scalar multiplication in a vector space depends onF.Thus when we need to be precise, we will say thatVis a vector space overFinstead of saying simply thatVis a vector space.For example,Rnis a ...