Course Slides
MA1034 • 8 Sessions
Vector Spaces
Formal definition of vector spaces and subspaces, the 10 closure axioms and applied examples in production systems.
Generating Sets & Dimension
Linear combinations, generating sets, linear independence, bases and dimension of subspace of constraints.
Linear Transformations
Linear transformations, fundamental subspaces (Null Space and Image) and the Rank-Nullity Theorem.
Matrix Representation
Matrix representation of transformations with respect to arbitrary bases $[T]_B^C$, coordinate vectors and change of basis.
Eigenvalues & Eigenvectors
Eigenvalues and eigenvectors in dynamic systems, characteristic equation and search for steady states.
Diagonalization
Change of basis matrices, diagonalization of operators $A = PDP^{-1}$ and matrix powers in assembly lines.
Orthogonality
Inner product, norm, angles, orthogonal vectors and orthogonal projections in product quality metrics.
Gram-Schmidt Process
Construction of orthonormal bases with the Gram-Schmidt process and its application in the orthogonalization of correlated data.