Chapter 2  Vectors Scalar  Vector  Transpose  Sum & Subtraction  Multiplication Debugged Codes
Chapter 3  Vector Multiplication Vector dot product, Algebra and Geometry  Linear weighted combinations  The outer product  Hadamard multiplication  Cross product  Unit vectors Debugged Codes
Chapter 4  Vector Spaces Dimensions and fields  Vector spaces  Subspaces and ambient spaces  Subsets  Span  Linear independence Debugged Codes
Chapter 5  Matrices Interpreting matrices  Matrix term and notation  Matrix dimensionalities  The transpose operation  Matrix zoology  Matrix addition and subtraction  Scalarmatrix multiplication  "Shifting" a matrix  Diagonal and trace Debugged Codes


Chapter 6  Matrix Multiplication "Standard" multiplication  Multiplication and equations  Multiplication with diagonals  LIVE EVIL  Matrixvector multiplication  Creating symmetric matrices  Multiply symmetric matrices  Hadamard multiplication  Frobenius dot product  Matrix norms  Matrix asymmetry index  What about matrix division? Debugged Codes
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, A^{T}, A^{T}A, and AA^{T}  Rank of random matrices  Boosting rank by "shifting"  Rank difficulties  Rank and span Debugged Codes
Chapter 8  Matrix spaces Column space od a matrix  Column space: A and AA^{T}  Determining whether v ∈ C(A)  Row space of a matrix  Row spaces of A and A^{T}A  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 Debugged Codes
Chapter 9  Complex numbers Complex numbers and  What are complex numbers?  The complex conjugate  Complex arithmetic  Complex dot product  Special complex matrices Debugged Codes
