MATH 2270: Linear Algebra

A comprehensive foundational course in linear algebra. Explores systems of linear equations, Gaussian elimination, matrix operations, invertible matrices, determinants, vector spaces, subspaces, basis and dimension, linear transformations, eigenvalues, eigenvectors, diagonalization, inner products, and orthogonality.

• Systems of linear equations: Gaussian elimination, row echelon form, matrix inverses, and LU decomposition in MATH 2270
• Vector space theory: linear independence, span, basis vectors, dimension, null space, and column space
• Linear transformations: matrix representations, kernel and range, coordinates, and change of basis transformations
• Spectral theory and applications: eigenvalues, eigenvectors, characteristic polynomials, and matrix diagonalization in Linear Algebra