Matrices power machine learning, computer graphics, and quantum computing. Learn to transform, solve, and decompose linear systems.
Neural networks are matrix multiplications at scale.
Rotation, scaling, and projection transformations.
PCA, SVD, and dimensionality reduction.
What: Matrix operations, Diagonal, Triangular, Symmetric, Hermitian forms.
Why: Understand the basic objects and their algebraic properties.
What: Minors, Cofactors, Cramer's Rule, Adjoint, Inverse.
Why: The determinant defines a matrix's "scale"; inverses reverse operations.
What: Linear Independence, Gaussian Elimination, Rank, Homogeneous Systems, LU Decomposition.
Why: Solve the fundamental equation Ax = B.
What: Eigenvalues, Eigenvectors, Cayley-Hamilton Theorem.
Why: Find directions where transformations only scale without rotating.