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Welcome to Linear Algebra Systems of Linear Equations and Matrices Introduction to Systems of Linear Equations Solving Systems of Linear Equations Gaussian Elimination Method Introduction to Matrices and Matrix Algebra Matrix Multiplication Algebraic Properties of Matrices Invertible Matrices Method for finding the inverse of a matrix Special Matrices: Diagonal, Triangular and Symmetric Exercises with Solutions Determinants of Matrices Introduction to Determinants Determinants by Cofactor Expansion Computational Aspects of the Determinants by Elementary Operations More Properties of Determinants: Application to the Matrix Inverse Application of Determinants: Cramer's Formulas Exercises with Solutions Euclidean vector Spaces: ℝ2, ℝ3 and ℝn Vectors Norm, Dot Product and Euclidean Distance Orthogonality Abstract Vector Spaces Real Vector Spaces Subspaces Linear Independance Basis and Associated Coordinates Dimension Change of Basis Row, Column and Null Spaces Rank and Nullity of Matrices Some Basic Matrix Transformations Eigenvalues and Eigenvectors Definitions Diagonalization Inner Product Spaces or Hilbert Spaces Inner Products Gram-Schmidt Process QR-Decomposition Best Approximation and Least Squares Method