Linear Algebra

Learning outcomes

What learners can expect

1. Solve and interpret linear systems using elimination, pivots, rank, and matrix structure.
2. Reason with span, independence, basis, coordinates, subspaces, null spaces, and column spaces.
3. Represent and compose linear maps, change bases, and interpret common geometric transformations.
4. Use determinants as oriented volume scaling and as one equivalent test of square-matrix invertibility.
5. Compute eigenvalues/eigenvectors, diagonalize when possible, and analyse repeated linear dynamics.
6. Use inner products, Gram-Schmidt, QR intuition, and orthogonal projection.
7. Solve overdetermined systems by least squares and interpret residuals, projection, and conditioning.
8. Apply linear algebra to stochastic-style dynamics, quadratic forms, and synthetic sensor inverse problems.