Create Time: 23th Dec 2023
Title: "[[Orthogonality]]"
status: DONE
Author:
- AllenyGy
tags:
- Orthogonality
- Lec3
- NOTE
- LinearAlgebra
created: 2023-12-23T02:12
updated: 2024-04-08T22:58
If 𝑋 and y are orthogonal subspaces of
If y is a subspace of
The column space of
Thus,
If A is an m×n matrix, then
If S is a subspace of
Furthermore, if {
If S is a subspace of
Summary
For ANy vector space 𝑉, there is an abstract definition of inner product ⟨x,y⟩: it must satisfy
If {
If 𝐵={
We say that 𝐵 is an orthonormal basis for S.
Let {
In other words, for any x∈𝑉
[5]
If the column vectors of m×n matrix A form an orthonormal set of vectors in
If {
An n×n matrix 𝑄 is an orthogonal matrix if and only if
If the column vectors of m×n matrix A form an orthonormal set of vectors in