Linear Algebra Basics: Terminologies, Special Matrices, Arithmetic, Matrix Function and Derivative

Definition of a matrix, its diagonal, transpose, and trace, as well as special types of matrices, including square vs. non-square (fat or tall), diagonal, upper and lower triangular, sparse vs dense (and definition of sparsity), identity, zero, symmetric and skew-symmetric followed by matrix arithmetic (addition and subtraction, multiplication and power), functions of matrices, derivatives of matrices and the skew-symmetric operator for a vector are all discussed in this video.
Square and Non-Square Matrices: 3:43
Main Diagonal and Trace of a Matrix: 5:40
Diagonal and Triangular Matrices: 7:51
Identity and Zero Matrices: 11:30
Spare Matrices and Sparsity: 12:38
Matrix Addition, Subtraction, and Multiplication: 16:34
Powers of a Matrix: 26:53
Properties of Matrix Product and Addition/Subtraction: 33:45
Matrix Transpose, Symmetric and Skew Symmetric Matrices: 37:44
Skew Symmetric Matrix of a Vector and Cross Product Using It: 44:08
Derivative of a Matrix: 48:25
Functions of Matrices: 50:04