6-Day Intensive Course

ETS 1.0 Linear Algebra

Learn linear algebra concepts guided by JAM/GATE/JRF PhD experts, having an exam-ready syllabus and live sessions with certification.

November 17-22, 2025
Enroll Now
Certificate on Completion
6
Days
12
Sessions
15
Hours Total
100+
Practice Problems

Why This Course?

Linear Algebra is the language of modern mathematics, data science, machine learning, quantum computing, and engineering. This intensive course builds both theoretical depth and practical problem-solving skills essential for IIT JAM, CUET PG, and advanced research.

Vector Space & Transformations

Master the foundations: basis, dimension, linear independence, and transformation theory.

Eigenvalues & Matrix Theory

Deep dive into eigenvalues, eigenvectors, diagonalization, and advanced matrix decompositions.

Real-World Applications

Connect to machine learning, quantum mechanics, data analysis, and computational algorithms.

Your Learning Journey

From fundamental concepts to advanced applications

Vector Space Foundations

Understand vector spaces, subspaces, linear independence, basis, and dimension with rigorous proofs.

Linear Transformations & Matrices

Matrix representation, range space, null space, and the rank-nullity theorem.

Systems of Linear Equations

Solve systems efficiently, understand consistency conditions, and apply Gaussian elimination techniques.

Eigenvalues & Cayley-Hamilton

Compute eigenvalues, eigenvectors, diagonalization, and master the Cayley-Hamilton theorem.

Special Matrices

Explore symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal, and unitary matrices.

Certificate of Completion

Earn a verified certificate showcasing your expertise in Linear Algebra

Recognized by industry professionals & academic institutions

Comprehensive Curriculum

Six intensive modules covering theory, computation, and applications

Module 1: Vector Spaces & Linear Independence

1 Vector Spaces & Subspaces

  • • Definition and examples of vector spaces
  • • Subspaces and subspace criteria
  • • Span of vectors

2 Linear Dependence & Independence

  • • Linear combinations and dependence
  • • Testing for independence
  • • Maximal independent sets

3 Basis & Dimension

  • • Definition of basis
  • • Dimension theorem
  • • Standard and ordered bases
Competition Focus

IIT JAM & CUET PG problems on dimension and basis identification

Module 2: Linear Transformations & Matrix Representation

1 Linear Transformations

  • • Definition and properties
  • • Kernel and image
  • • Composition of transformations

2 Matrix Representation

  • • Representation with respect to ordered basis
  • • Change of basis
  • • Similarity of matrices

3 Range Space & Null Space

  • • Computing null space and range
  • • Rank-nullity theorem
  • • Applications and examples
Competition Focus

Transformation problems and rank-nullity applications

Module 3: Matrices & Systems of Linear Equations

1 Matrix Operations

  • • Addition, multiplication, transpose
  • • Inverse of a matrix
  • • Elementary row operations

2 Systems of Linear Equations

  • • Gaussian elimination
  • • Row echelon and reduced row echelon form
  • • Consistency conditions

3 Rank & Determinants

  • • Computing rank of a matrix
  • • Determinant properties and computation
  • • Cramer's rule
Competition Focus

Rapid methods for solving systems and computing determinants

Module 4: Eigenvalues, Eigenvectors & Diagonalization

1 Eigenvalues & Eigenvectors

  • • Characteristic polynomial
  • • Computing eigenvalues and eigenvectors
  • • Algebraic and geometric multiplicity

2 Diagonalization

  • • Conditions for diagonalizability
  • • Similarity transformations
  • • Applications to matrix powers

3 Cayley-Hamilton Theorem

  • • Statement and proof
  • • Computing matrix inverses
  • • Applications to minimal polynomials
Competition Focus

Eigenvalue problems and Cayley-Hamilton applications in exams

Module 5: Special Matrices I - Symmetric & Hermitian

1 Symmetric Matrices

  • • Definition and properties
  • • Real eigenvalues and orthogonal eigenvectors
  • • Spectral theorem

2 Skew-Symmetric Matrices

  • • Properties and examples
  • • Eigenvalue structure

3 Hermitian & Skew-Hermitian Matrices

  • • Complex inner products
  • • Properties of Hermitian matrices
Competition Focus

Identifying special matrix types and their eigenvalue properties

Module 6: Special Matrices II - Orthogonal & Unitary

1 Orthogonal Matrices

  • • Definition and characterization
  • • Preservation of inner products
  • • Rotations and reflections

2 Unitary Matrices

  • • Definition and properties
  • • Applications in quantum computing

3 Final review

  • • Final review and exam strategies
Competition Focus

Comprehensive problem-solving and time management for IIT JAM/CUET PG

Course Features

Competition-Oriented

Previous year IIT JAM & CUET PG questions with expert solutions

Conceptual Depth

Rigorous proofs and mathematical intuition development

Industry Applications

Machine learning, quantum computing, data analysis connections

Computational Tools

Python/MATLAB demonstrations for numerical linear algebra

Interactive Sessions

Live problem-solving and Q&A with expert instructors

100+ Practice Problems

Comprehensive problem sets with detailed solutions

Learn from the Best

Your instructors are IIT JAM, GATE, and CSIR JRF qualified PhD holders with extensive academic and research backgrounds from India's premier institutions.

Target Audience

IIT JAM Mathematics aspirants
CUET PG Mathematics candidates
MSc/BS Mathematics students
Data science & ML enthusiasts

Prerequisites

Basic calculus and set theory
High school level matrices
Basic Mathematical maturity

No advanced prerequisites—we build from fundamentals

Career Pathways

Where linear algebra takes you

Academic Research

Pure & applied mathematics

Data Scientist

Machine learning engineer

Quantum Computing

Quantum algorithm specialist

Industry Analyst

Quantitative researcher

Enroll Today

Transform your understanding of Linear Algebra

₹665
₹950 after November 10, 2025
All inclusive • Certificate included
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