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CY-401 RGPV B.Tech

Introduction to Linear Algebra (ILA)

Previous year papers and the official syllabus are free to read, no account needed.

Previous Year Papers

6 papers, latest Jun 2025

Free
See all 6 papers

Syllabus, notes and important questions for CY-401

Syllabus units

Topics as the official RGPV syllabus lists them.

Unit 1 Direct sum of a vector space, Dual Spaces 5 topics
  • Direct sum of a vector space
  • Dual Spaces
  • Annihilator of a subspace
  • Quotient Spaces
  • Algebra of Linear transformations
Unit 1 notes
Unit 2 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 9 topics
  • 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
Unit 2 notes
Unit 3 Adjoint of a linear transformation, Inner product spaces, Eigenvalues and eigenvectors, Diagonalization, Invariant subspaces, Unitary and normal transformations, Spectral Theorem, Jordan canonical form 8 topics
  • 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
Unit 3 notes
Unit 4 Canonical forms, Similarity of linear transformations, Reduction to triangular forms, Nilpotent transformations, Primary decomposition theorem, Jordan blocks and Jordan forms, Invariants of linear transformations 7 topics
  • Canonical forms
  • Similarity of linear transformations
  • Reduction to triangular forms
  • Nilpotent transformations
  • Primary decomposition theorem
  • Jordan blocks and Jordan forms
  • Invariants of linear transformations
Unit 4 notes
Unit 5 Hermitian, Self adjoint, Unitary and normal linear transformation, Symmetric bilinear forms, Skew symmetric bilinear forms, Group preserving bilinear forms 6 topics
  • Hermitian linear transformations
  • Self‑adjoint linear transformations
  • Unitary and normal linear transformations
  • Symmetric bilinear forms
  • Skew‑symmetric bilinear forms
  • Group‑preserving bilinear forms
Unit 5 notes
Unit 6 Unit 3 5 topics
  • Inner product spaces
  • adjoints
  • unitary and normal transformations
  • spectral Theorem
  • Jordan canonical form
Read the full syllabus

Exam insights

Counted from 6 past CY-401 papers.

Marks asked per paper, by unit

  • Unit 1 Direct sum of a vector space 28 marks
  • Unit 2 Characteristic values and characteristic polynomials 28 marks
  • Unit 3 Adjoint of a linear transformation 20 marks
  • Unit 4 Canonical forms 19 marks
  • Unit 5 Hermitian, Self adjoint, Unitary and normal linear transformation 18 marks

Average marks of the questions from each unit in one paper. You answer only some of them, so the total is more than the paper’s maximum.

Asked again and again

  1. Show that a given $3\times 3$ matrix / linear operator is diagonalizable and find the diagonal matrix and the transforming (modal) matrix $P$.

    Asked 3 times: 2024, 2023, 2022

  2. Prove that a linear operator on an $n$-dimensional vector space with $n$ distinct eigenvalues / characteristic values is diagonalizable.

    Asked 2 times: 2025, 2023

  3. Verify the Cayley-Hamilton theorem for a given $2\times 2$ matrix by finding its characteristic polynomial and substituting the matrix

    Asked 2 times: 2024

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