Become a Linear Algebra Master

What you'll learn
Operations on one matrix, including solving linear systems, and Gauss-Jordan elimination
Operations on two matrices, including matrix multiplication and elimination matrices
Matrices as vectors, including linear combinations and span, linear independence, and subspaces
Dot products and cross products, including the Cauchy-Schwarz and vector triangle inequalities
Matrix-vector products, including the null and column spaces, and solving Ax=b
Transformations, including linear transformations, projections, and composition of transformations
Inverses, including invertible and singular matrices, and solving systems with inverse matrices
Determinants, including upper and lower triangular matrices, and Cramer's rule
Transposes, including their determinants, and the null (left null) and column (row) spaces of the transpose
Orthogonality and change of basis, including orthogonal complements, projections onto a subspace, least squares, and changing the basis
Orthonormal bases and Gram-Schmidt, including definition of the orthonormal basis, and converting to an orthonormal basis with the Gram-Schmidt process
Eigenvalues and Eigenvectors, including finding eigenvalues and their associate eigenvectors and eigenspaces, and eigen in three dimensions
Requirements
You should be comfortable with the Fundamentals of Math, like arithmetic (addition, subtraction, multiplication, division) of positive and negative numbers, fractions, and decimals.
You should be comfortable with Algebra, like equation solving, graphing, and factoring, plus exponents and roots.
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