Methods For Solving Systems of Linear Equations# Norms of Vectors And Matrices, Iterative Methods. Inner Product Spaces# Cauchy-schwarz Inequality, Orthogonal Complement and Gram-schmidt Process, Orthogonal Projections, Orthonormal Bases, Bessel Inequality, Qr Decomposition. Operators in Inner Product Spaces# Linear Functionals, Riesz Theorem and The Adjoint Operator, Normal Operators, Self-adjoint Operators, Unitary Operators, Positive Operators. Spectral Decomposition Theorem, Orthogonal Diagonalization, Jordan Normal Form, Polar Decomposition Theorem, Svd Decomposition, Cholesky Decomposition. Min-max Theorem and Rayleigh Quotient. Bilinear And Quadratic Forms, Polarization Identity, Classification of Quadratic Forms Over The Reals# Matrix Congruence, Sylvester's Law of Inertia. Tensor Calculus.

Faculty: Mathematics
|Undergraduate Studies

Pre-required courses

(104012 - Differential and Integral Calculus 1t and 104016 - Algebra 1/extended) or (104016 - Algebra 1/extended and 104036 - Differential and Integral Calculus 1t) or (104016 - Algebra 1/extended and 104031 - Calculus 1m) or (104016 - Algebra 1/extended and 104018 - Differential and Integral Calculus 1m) or (104016 - Algebra 1/extended and 104041 - Differential and Integral Calculus 1m1) or (104016 - Algebra 1/extended and 104042 - Differential and Integral Calculus 1m2)


Course with no extra credit

104168 - Algebra B 104174 - Algebra Bm 234125 - Numerical Algorithms


Semestrial Information