linear algebra - wordpress.com...2018/08/02 · group theory and linear algebra linear algebra...
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Group Theory and Linear Algebra
Linear Algebra
Division of Integers
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Modular Arithmetic
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Algebraic Fields
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Vector Space
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Linear Independence
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Linear Transformations
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Matrix Representations
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Minimal Polynomials
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Characteristic Polynomials
Jordan Normal Form
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Inner Product Spaces
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Orthonormal Bases
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Orthogonal Complement
Adjoints
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Spectral Theorem
Matrix Square Roots
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Group Theory
Group Definitions
Examples of Groups
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Subgroups
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Isomorphisms
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Direct Product
Orders of Subgroups
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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
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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