Introduction to Linear Algebra (ILA)
CY-401-
Unit 1Direct sum of a vector space, Dual Spaces
Direct sum of a vector space · Dual Spaces · Annihilator of a subspace · Quotient Spaces · Algebra of Linear transformations
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Unit 2Characteristic values and characteristic polynomials, diagonalizable transformations, annihilating polynomials, Cayley‑Hamilton theorem, invariant subspaces and triangular form, simultaneous triangularization and diagonalization, direct sum decompositions, invariant direct sums, primary decomposition theorem
Characteristic values and characteristic polynomials · Diagonalizable transformations · Annihilating polynomials · Cayley‑Hamilton theorem · Invariant subspaces and triangular form · Simultaneous triangularization and diagonalization · Direct sum decompositions · Invariant direct sums · Primary decomposition theorem
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Unit 3Adjoint of a linear transformation, Inner product spaces, Eigenvalues and eigenvectors, Diagonalization, Invariant subspaces, Unitary and normal transformations, Spectral Theorem, Jordan canonical form
Adjoint of a linear transformation · Inner product spaces · Eigenvalues and eigenvectors of a linear transformation · Diagonalization · Invariant subspaces · Unitary and normal transformations · Spectral Theorem · Jordan canonical form
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Unit 4Canonical forms, Similarity of linear transformations, Reduction to triangular forms, Nilpotent transformations, Primary decomposition theorem, Jordan blocks and Jordan forms, Invariants of linear transformations
Canonical forms · Similarity of linear transformations · Reduction to triangular forms · Nilpotent transformations · Primary decomposition theorem · Jordan blocks and Jordan forms · Invariants of linear transformations
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Unit 5Hermitian, Self adjoint, Unitary and normal linear transformation, Symmetric bilinear forms, Skew symmetric bilinear forms, Group preserving bilinear forms
Hermitian linear transformations · Self‑adjoint linear transformations · Unitary and normal linear transformations · Symmetric bilinear forms · Skew‑symmetric bilinear forms · Group‑preserving bilinear forms
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Unit 6Unit 3
Inner product spaces · adjoints · unitary and normal transformations · spectral Theorem · Jordan canonical form