About What's the big idea of Linear Algebra? **Course Intro**

Mathematics in general Mathematics for nonmathematicians (engineering, social sciences, etc.) Is Vector B in Span of Vectors A1 A2 and A3 in Linear Algebra Linear Algebra Matrix Vector Multiplication Equation Ax equals B in Linear Algebra Linear Algebra Matrix Vector Multiplication Example in Linear Algebra Linear Algebra solutions to Ax=b and homogeneous systems Ax=0 visualized in vector space Three nice properties of homogeneous systems of linear equations Determining Linear Independence vs Linear Dependence Linear Independence in Linear Algebra Linear Transformations in Linear Algebra Linear Algebra Matrix Transformations and Linear Transformations Equivalence Linear Algebra: Deriving Rotation and Reflection Matrices from Standard Basis Vectors in R2 Matrix Multiplication in Linear Algebra Linear Algebra: Elementary Matrices Corresponding to Row Operations in Identity Matrix 2x2 Matrix Inverse Formula in Linear Algebra Determinant Calculation in Linear Algebra via Expansion Along Any Row or Column Span and Basis in Polynomials of Degree Less Than or Equal to n for Linear Algebra Finding Basis for Nullspace and Column Space in Linear Algebra Writing Vectors in Basis B using Invertible Matrices for Linear Algebra Linear Algebra Grid Lines Defined by Integer Linear Combinations of Standard Basis Vectors Dimension Definition in Linear Algebra via Basis Vector Counting Computing Dimensions of Null Space and Column Space in Linear Algebra The Rank Dimension Theorem in Linear Algebra Mathematics and visual arts Linear Algebra Eigenvalues Eigenvectors Geometric Interpretation Scaling Factor Nonzero Vectors Linear Algebra Diagonal Matrix Computation and Properties Linear Algebra Diagonalization Using Eigenvectors and Eigenvalues for Square Matrices Complex Eigenvalues and Eigenvectors in Linear Algebra: Full Example for Diagonalization Matrix A Linear Algebra diagonalization visualization Similar matrices have similar properties Vector Angle and Orthogonality in Linear Algebra using Dot Product Definitions Linear Algebra Orthogonal Basis Coefficient Calculation via Dot Products Orthogonal Projections in Linear Algebra Gram-Schmidt Orthogonalization in Linear Algebra