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Group Theory and Linear Algebra
Linear Algebra
Division of Integers
2
Modular Arithmetic
3
Algebraic Fields
4
Vector Space
5
Linear Independence
6
Linear Transformations
7
Matrix Representations
8
Minimal Polynomials
9
10
Characteristic Polynomials
Jordan Normal Form
11
12
Inner Product Spaces
13
Orthonormal Bases
14
15
Orthogonal Complement
Adjoints
16
17
Spectral Theorem
Matrix Square Roots
18
Group Theory
Group Definitions
Examples of Groups
19
Subgroups
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Isomorphisms
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Direct Product
Orders of Subgroups
23
Cosets
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Quotient Groups
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Homomorphisms
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Group Action
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Orbit-Stabalizer Relation
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Conjugation
29
Sylow Theorems
Isometries
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Euclidean Isometries
Random Stuff
Not every matrix has a square root, e.g:
Group of roots of unity is cyclic with generator
Every cyclic group is abelian
Vectors in Gram-Schmidt don't need to be orthogonal, just linearly independent
A square matrix is invertible if its determinant is non-zero
has only the trivial solution