Class notes
MAT2611- CHEAT NOTES
- Course
- Linear Algebra 2 (MAT2611)
- Institution
- University Of South Africa (Unisa)
This document serves as a simple and effective way to ensure that you get that distinction you've always been wanting!
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
Seller
Follow
Content preview
LINEAR ALGEBRA 2: CHEAT SHEETBY SHERWIN NAIDOO
1. Eigenvalues and Eigenvectors
• Eigenvalue equation: Ax = λx
• Characteristic Polynomial: 𝑑𝑒𝑡(A − 𝜆I) = 0
• Eigenvalues (λ): Solutions to the characteristic polynomial.
• Eigenvectors (x): refers to non-zero vectors satisfying, Ax = 𝜆x.
2. Diagonalization:
• Diagonalizable matrix: A = PDP-1 , where D is a Diagonal matrix and P is an
invertible matrix of eigenvectors.
• Process:
➢ Find Eigenvalues λ
➢ Find Corresponding Eigenvectors X
➢ Construct P from the eigenvectors
➢ D contains the eigenvalues on the diagonal
3. Inner product squares:
• Inner product: 〈u, v〉
• Norm: ‖v‖ = √〈u, v〉
• Orthogonality: u ⊥ v if 〈u, v〉 = 0
〈v,u〉
• Orthogonal Projection: proju v = 〈v,u〉 u
4. Gram-Schmidt process:
Given the Basis {v1 , v2 , . . . , vn }:
• u1 = v1
• u2 = v2 − proju1 v2
• u3 = v3 − proju1 v3 − proju2 v3
Continue similarly for 𝑢𝑛
5. Orthogonal matrices:
• Orthogonal Matrix: Q such that QT Q = QQT = I
• Properties:
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller sherwinnaidoo. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R85,33. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67474 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now