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IIT JAM Linear Algebra 1st Edition by Vikas Deoarshi ISBN 9383668067 9789383668069

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IIT JAM Linear Algebra 1st Edition Vishal Deoarshi Digital Instant Download

Author(s): Vishal Deoarshi, Vikas Deoarshi
ISBN(s): 9789383668069, 9383668067
Edition: 1
File Details: PDF, 7.70 MB
Year: 2016
Language: english
SKU: EB-36418578 Category: Tags: ,

IIT JAM Linear Algebra 1st Edition by Vikas Deoarshi – Ebook PDF Instant Download/Delivery: 9383668067, 9789383668069
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Product details:

ISBN 10: 9383668067 
ISBN 13: 9789383668069
Author: Vikas Deoarshi

This book will go a long way in helping students in their preparation of M.Sc and Ph.D Entrance Exam like IIT-JAM, TIFR, CMI,ISI,CSIR-NET, GATE etc. The book has been divided into five chapters. The total contents are given below : 1) Algebra of Matrices 2) Vector Space and Linear Equations 3) Orthogonality 4) Eigenvalues and Eigenvectors 5) Linear Transformation Author: OUR SENIOR FACULTY (MR.VISHAL DEOARSHI) ABOUT FACULTY: MORE THAN 14 YEARS OF TEACHING EXPERIENCE IN PHYSICS & MATHS AT GRADUATE & POST GRADUATE LEVEL.
 

IIT JAM Linear Algebra 1st Table of contents:

Chapter 1: Vector Spaces

  • 1.1 Introduction to Vector Spaces

  • 1.2 Subspaces

  • 1.3 Linear Combinations and Span

  • 1.4 Linear Dependence and Independence

  • 1.5 Basis and Dimension

  • 1.6 Row Space, Column Space, and Null Space

  • 1.7 Quotient Spaces

  • 1.8 Direct Sum of Subspaces

Chapter 2: Matrices

  • 2.1 Types of Matrices

  • 2.2 Matrix Operations

  • 2.3 Transpose and Conjugate Transpose

  • 2.4 Elementary Row and Column Operations

  • 2.5 Rank of a Matrix

  • 2.6 Inverse of a Matrix

  • 2.7 Partitioned Matrices

  • 2.8 Applications to Systems of Linear Equations

Chapter 3: Linear Transformations

  • 3.1 Definition and Examples

  • 3.2 Matrix of a Linear Transformation

  • 3.3 Kernel and Image

  • 3.4 Rank-Nullity Theorem

  • 3.5 Change of Basis

  • 3.6 Isomorphisms

  • 3.7 Dual Spaces (Basics)

Chapter 4: Eigenvalues and Eigenvectors

  • 4.1 Characteristic Polynomial

  • 4.2 Diagonalizability

  • 4.3 Algebraic and Geometric Multiplicity

  • 4.4 Minimal Polynomial

  • 4.5 Cayley-Hamilton Theorem

  • 4.6 Invariant Subspaces

  • 4.7 Applications to Differential Equations

Chapter 5: Inner Product Spaces

  • 5.1 Inner Product and Norm

  • 5.2 Orthogonality

  • 5.3 Gram-Schmidt Process

  • 5.4 Orthogonal and Orthonormal Bases

  • 5.5 Orthogonal Projections

  • 5.6 Least Squares Approximation

  • 5.7 Adjoint of a Linear Operator

Chapter 6: Diagonalization and Canonical Forms

  • 6.1 Diagonalization of Matrices

  • 6.2 Orthogonal Diagonalization of Symmetric Matrices

  • 6.3 Jordan Canonical Form (Basics, optional for JAM)

  • 6.4 Spectral Theorem for Symmetric Matrices

Chapter 7: Determinants

  • 7.1 Definition and Properties

  • 7.2 Cofactor Expansion

  • 7.3 Effect of Row Operations

  • 7.4 Determinants and Invertibility

  • 7.5 Applications in Volume and Area

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Tags: Vikas Deoarshi, IIT JAM, Linear Algebra