Course Details

Course details of EE5120W
Course NoEE5120W
Course TitleApplied Linear Algebra I for EE
Course ContentLinear System of Equations: Gaussian elimination—ehelon forms—existence, uniqueness, and multiplicity of solutions in a system of linear equations.Vector Spaces: Definition—linear dependence and independence—spanning sets, basis, and dimension—definition of subspace—intersection and sum of subspaces—direct sums and embedding of subspaces.Linear Transformations: Definition—matrix representation of a linear transformation—the four fundamental subspaces associated with a linear transformation—system of linear equations revisited—change of bases—similarity transformations—invertible transformations.Inner Products: Definition, induced norm, inequalities, orthogonality—Gram-Schmidt orthogonalization process—orthogonal and rank one projections—unitary transformations and isometry.Eigen Decomposition: Eigenvalues and eigenvectors—Gerschgorin circles—characteristic polynomials and eigenspaces—diagonlizability conditions—invariant subspaces—spectral theorem—Rayleigh quotient.
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