What linear algebra is, Systems of linear equations and matrices, elementary row operations, inverse, matrix equations, determinant, LU factorization. Vectors in Euclidean n-space (Rn), linear combination and linear independence. Vector spaces, subspaces, bases and dimensions. Linear transformation, null space and range, isomorphism, matrix representation of linear transformation, and similarity. Eigenvalues and eigenvectors, diagonalization, Markov chain. Inner product spaces. The dot product on Rn, orthogonal bases, orthogonal complements. Applications.
