* ./2017-223/week-01/mat-223-week-1.pdf
* linear equations
* augmented matrices
* elementary row operations
* row echelon form (REF)
* reduced row echelon form (RREF)
* Gaussian algorithm
* solving linear systems
* consistent and inconsistent systems
* ./2017-223/week-01/mat-223-week-1c.pdf
* parametrized solutions
* parameters and rank
* homogeneous systems
* trivial solution
* column vectors
* basic solutions
* Week 2
* dimensions of a matrix
* matrix sum
* matrix product
* transpose
* column vector
* row vector
* n-dimensional euclidean space
* dot product
* Week 3
* handout
* matrix multiplication
* non-commutativity of matrix multiplication
* the plane
* linear maps acting on the plane
* matrix inversion
* determinant
* adjugate
* matrix inversion algorithm
* Fundamental Theorem of Linear Algebra
* Week 4
* handout
* linear transformations
* matrix of a linear map
* geometry of linear maps
* rotations
* determinants and co-factors
* row operations and determinants
* det(AB)=det(A)det(B)
* Week 5
* cofactor expansion
* matrix equations
* complex numbers
* complex plane
* modulus
* argument
* Euler's identity
* polar coordinates
* Week 6
* eigen-handout
* eigenvalues
* eigenvectors
* characteristic polynomials
* complex eigenvalues
* repeated eigenvalues
* basic eigenvectors
* multiplicity of eigenvectors
* diagonalization
* Week 7
* cartesian coordinate system
* lines and planes
* length
* geometric vectors
* parallelogram law
* parametric equation of a line
* intersection of lines
* dot products
* angles
* orthogonality
* projections
* Week 8
* lines and planes
* vector form of a plane
* parametric form of a plane
* normal to a plane
* plane containing two lines
* distance to a plane
* distance between two lines
* Week 9
* subspaces
* image of a linear transformation
* kernel of a linear transformation
* span of a set of vectors
* linear independence
* dimension
* bases
* Week 10
* cross product
* orthogonality
* orthonormal
* Pythagorean theorem in an orthonormal basis
* projection to an orthonormal bases
* Week 11
* exam practice
* rank of matrices
* column space
* row space
* properties of span
* invariance of row space under row operations
* Week 12
* orthogonal complement
* Gram-Schmidt orthogonalization algorithm
* similar matrices
* diagonalization
* eigenspaces