About Essence of linear algebra preview

Dot Products and Duality: Vectors as Linear Transformations Cross Product: Area, Orthogonality, and the Right-Hand Rule Linear Independence and Span in Vector Spaces Nonsquare Matrices: Transforming Vectors Between Dimensions Linear Transformations and Matrices in Two Dimensions Cross Product Geometry via Dual Vectors and Determinants Linear Transformations of 3D Vectors via Matrix Representations Eigenvalues and Eigenvectors Definitions in Linear Algebra Eigenvalues and Eigenvectors in Linear Algebra Mathematics for nonmathematicians (engineering, social sciences, etc.) Change of Basis via the Invertible Transition Matrix Solving Systems of Linear Equations Algebraically Abstract Vector Spaces: The Eight Axioms Determinant: Volume Scaling and Orientation of a Linear Transformation Matrix Multiplication as Composition of Linear Transformations