CY-401 Introduction to Linear Algebra Notes
5 notes for Introduction to Linear Algebra, unit by unit.
Notes for CY-401
- Unit 1 · Short notes Direct 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
- Unit 2 · Short notes 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 Characteristic values and characteristic polynomials · Diagonalizable transformations · Annihilating polynomials · Cayley‑Hamilton theorem · Invariant subspaces and triangular form · Simultaneous triangularization and diagonalization
- Unit 3 · Short notes Adjoint 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
- Unit 4 · Short notes Canonical 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
- Unit 5 · Short notes Hermitian, 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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