Page 160 - FINAL_HANDBOOK_20242025

Faculty of Science Handbook, Academic Session 2024/2025

SIM3004 Penrose inverses, the best
ADVANCED LINEAR approximation solutions, least
ALGEBRA squares solutions. Kronecker
products of matrices,
Inner product spaces, the permutations, matrix functions
Cauchy-Schwarz inequality, of Kronecker products, Schmidt
the Gram-Schmidt rank and decompositions.
orthogonalization process,
orthogonal complements, Assessment:
orthogonal projections. Adjoint Continuous Assessment: 40%
operators, normal operators, Final Examination: 60%
self-adjoint operators, unitary
operators, positive definite
operators. Bilinear forms, SIM3006
congruence, rank, Sylvester’s ALGEBRA II
law of inertia, classification of
symmetric bilinear forms, real This is a second course in
quadratic forms. The Schur abstract algebra and will cover
triangularization theorem, the more advanced topics on
primary decomposition groups and rings. Topics on
theorem, the Jordan canonical groups include the
form. isomorphism theorems,
various subgroups such as the
Assessment: centre and commutator
Continuous Assessment: 40% subgroups, finitely generated
Final Examination: 60% abelian groups, automorphism
groups, permutation groups,
and p-groups.
SIM3005
MATRIX THEORY For rings, the focus is on
commutative rings. Topics on
Rank and nullity of matrices, rings include the maximal and
Sylvester’s law inequality, the prime ideals, polynomial rings,
Frobenius inner product, the irreducible polynomials and the
Gram-Schmidt process, the unique factorization theorem.
continuity argument. Rank and
full rank decompositions, LU Assessment:
and QR decompositions, Continuous Assessment: 40%
spectral decompositions, Final Examination: 60%
singular value decompositions,
polar decompositions,
Cholesky decompositions.
Generalized inverses, Moore-

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