🧊 Essence of Linear Algebra
✖️ MIT 18.06 Linear Algebra
Linear Algebra | Mathematics | MIT OpenCourseWare
👨🏫 Professor Dave Explains Linear Algebra
Systems of Linear Equations
Operations with Matrices
Addition
Scalar Multiplication
Matrix Multiplication
Transpose and Symmetric Matrices Definition
Gauss Elimination and Gauss-Jordan Elimination
Homogeneous System of Linear Equations
Inverse of a Matrix
Singular Matrices
Solving $Ax = b$ using $A^{-1}$
Determinant of a Matrix
Properties of determinants
Determinant of a diagonal matrix
Minors and Cofactors
Adjoint of a Matrix
Inverse of a Matrix using $adj$
Using Cramer’s rule to solve a system of linear equations
Vector Spaces
Subspaces
Linear Combination of vectors
Spanning Sets
Linear Independence
Row Space, Column Space, and Nullspace of a Matrix
Rank and Nullity
Basis, Dimension
Coordinate Representation Relative to a Basis
Inner Product Spaces, Norm and Dot Product
Unit Vector
Cauchy-Schwartz Inequality
Distance between two vectors
Angle between two vectors
Orthogonal Vectors
Triangle Inequality
Orthonormal Basis
Gram–Schmidt Orthonormalization Process
Eigenvalues and Eigen vectors
Diagonalization
Linear Transformations
Inverse of Linear Transformations
Kernel and Range of Linear Transformation