Linear Algebra Exam 2

a starting point for exam 2 studying

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Topics

The different concepts we should know for the exam

Eigen-stuff

Eigen values

Eigen vectors

Eigen spaces

Characteristic Polynomials

Diagonalization

Orthogonal Diagonalization

Similarity

Spectral Theorem

Multiplicity

Matrix Power

Linear Transformations

Rotation

Reflection

Stretching

Dilation

Matrix Representation

Fundamental Theorem Of Linear Algebra

Determinants

Cofactor Expansion

Properties

• $\det (A^{-1})=\frac{1}{\det A}$
• $\det (A^T)=\det (A)$
• $\det (AB)=\det (A)\det (B)$

Elementary Matrices

Quadratic Forms

Matrix Form

Classification

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Exam Structure

How the exam topic will be split on the exam

In-Person Portion

1. Determinants and Properties
2. Matrix Powers, Quadratic Forms, Multiplicity

Online Portion

3. Linear Transformations
4. Diagonalizability
   • No deficient eigenvalues (multiplicity)
5. Diagonalization Process (orthogonal)