Brief content of the courses
Vectors and Vector Equations of Lines & Planes
System of Linear Equations. Gauss-Jordan elimintation.
Determinant of matrices and its properties.
Eigenvalues and Eigenvectors.
Nullspace (Kernel) and the Column space (Image) of Matrices
Diagonalization, Power Method
Orthogonalization. QR decomposition.
Singular Value Decomposition.
Course description
Tentative Course Outline
Press "expand" to see the content; Press the name of a topic to see the video lectures and online quizzes;Vectors in a matrix form. Column vectors.
Scalar product and the angle between the vectors.
Vector theorems. Cauchy-Schwarz theorem.
Vector equations of lines & planes
Point-normal equation of planes
Linear combinations of vectors define lines, planes and spaces
Definition and notation
Homogeneous system of Linear Equations
Three elementary row operations
Rwo echelon form
Gauss-Jordan elimination
Matrix multiplication
Inverse of a matrix
Elementary matrices
Substituting elementary row operations with the elementary matrices
Diagonal matrices and their inverses
Elimination matrices and their inverses
Permutation matrices and their inverses
Properties of Determinants
Evaluate determinants using the Gauss elimination
Cofactors
Cramer's rule
Vector subspaces
Column spaces
Null spaces