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Chapter 2 - Vectors
Scalar - Vector - Transpose - Sum & Subtraction - Multiplication
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Chapter 3 - Vector Multiplication
Vector dot product, Algebra and Geometry - Linear weighted combinations - The outer product - Hadamard multiplication - Cross product - Unit vectors
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Chapter 4 - Vector Spaces
Dimensions and fields - Vector spaces - Subspaces and ambient spaces - Subsets - Span - Linear independence
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Chapter 5 - Matrices
Interpreting matrices - Matrix term and notation - Matrix dimensionalities - The transpose operation - Matrix zoology - Matrix addition and subtraction - Scalar-matrix multiplication - "Shifting" a matrix - Diagonal and trace
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Chapter 6 - Matrix Multiplication
"Standard" multiplication - Multiplication and equations - Multiplication with diagonals - LIVE EVIL - Matrix-vector multiplication - Creating symmetric matrices - Multiply symmetric matrices - Hadamard multiplication - Frobenius dot product - Matrix norms - Matrix asymmetry index - What about matrix division?
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Chapter 7 - Rank
Six things about matrix rank - Interpretations of matrix rank - Computing matrix rank - Rank and scalar multiplication - Rank of added matrices - Rank of multiplied matrices - Rank of A, AT, ATA, and AAT - Rank of random matrices - Boosting rank by "shifting" - Rank difficulties - Rank and span
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Chapter 8 - Matrix spaces
Column space od a matrix - Column space: A and AAT - Determining whether v ∈ C(A) - Row space of a matrix - Row spaces of A and ATA - Null space of a matrix - Geometry of the null space - Orthogonal subspaces - Matrix space orthogonalities - Dimensionalities of matrix spaces - More on Ax = b and Ay = 0
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Chapter 9 - Complex numbers
Complex numbers and - What are complex numbers? - The complex conjugate - Complex arithmetic - Complex dot product - Special complex matrices
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