Matrices Book by AR Vasishtha PDF Download 2023 [Krishna Series]

“Krishna Series Matrices” by A. R. Vasishtha is a specific book on the topic of matrices. It is likely a part of a series of textbooks called “Krishna Series” which is popular in India. So, you can download the PDF format of this Matrices Book by AR Vasishtha from the link which is given below.

The book focuses on the topic of matrices and its applications, including matrix algebra, determinants, inverses, and systems of linear equations. It likely includes clear explanations of the concepts, detailed examples and exercises, and coverage of both the theoretical and computational aspects of matrices.

The book is intended for use in a college-level course on linear algebra or mathematics. It also includes solved and unsolved problems to help students test their understanding of the material.

Krishna Series Matrices Book by AR Vasishtha Useful for

“Krishna Series Matrices” by A. R. Vasishtha is likely intended for use as a textbook for a college-level course on linear algebra or mathematics. The book provides a comprehensive introduction to the topic of matrices and its applications, including matrix algebra, determinants, inverses, and systems of linear equations. This book would be useful for students studying mathematics, physics, engineering, computer science, or other fields that use matrix algebra.

It will also be beneficial for students preparing for competitive exams in mathematics like IIT JAM, NBHM, CUET PG, TIFR, etc, or engineering. The book’s clear explanations, detailed examples, and exercises make it an excellent resource for students to learn and understand the concepts of matrices and its applications.

Krishna Series Matrices Book by AR Vasishtha: Features

“Krishna Series Matrices” by A. R. Vasishtha is likely to include the following features:

  1. Comprehensive coverage of the topic of matrices, including matrix algebra, determinants, inverses, and systems of linear equations.
  2. Clear explanations of the concepts and theorems, with the use of solved examples.
  3. Detailed exercises and problems to help students understand and apply the concepts.
  4. Coverage of both the theoretical and computational aspects of matrices, providing a good balance between theory and practice.
  5. Use of numerous solved examples, illustrations, and figures to make the subject more understandable.
  6. A comprehensive introduction to the subject matter and the development of the subject in a logical and structured manner.
  7. The book is written in a style that is easy to understand and follow.
  8. The book also includes a number of solved and unsolved problems to help students test their understanding of the material.
  9. It is likely intended for use in a college-level course on linear algebra or mathematics
  10. The book is a part of “Krishna Series” which is known for its quality, clarity, and accessibility, making it a popular choice for students and teachers in India.

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Download Krishna Series Matrices Book by AR Vasishtha PDF

AuthorA. R. Vasishtha & A. K. Vasishtha
PublicationKrishna’s Educational Publisher, Since 1942
Total Pages384 Pages
LanguageEnglish
Pdf QualityGood
File typePdf

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Krishna Series Matrices Book by AR Vasishtha PDF: Chapter Content

The Krishna series matrices book pdf contains the following chapters and topics.

Chapter 1: Algebra of MatricesBasic concepts
Matrix
Square matrix
Unit matrix or Identity Matrix
Null or zero matrix
Submatrices of a matrix
Equality of two matrices
Addition of matrices
Multiplication of a matrix by a scalar
Multiplication of two matrices
Triangular, Diagonal, and Scalar Matrices
Trace of a Matrix
Transpose of a Matrix
Conjugate of a Matrix
Transposed conjugate of a Matrix
Symmetric and skew-symmetric matrices
Hermitian and Skew-Hermitian Matrices
Chapter 2: DeterminantsDeterminants of order 2
Determinants of order 3
Minors and cofactors
Determinants of order n
Determinant of a square matrix
Properties of Determinants
Product of two determinants of the same order
System of non-homogeneous linear equations (Cramer’s Rule)
Chapter 3: Inverse of a MatrixAdjoint of a square matrix
Inverse or Reciprocal of a Matrix
Singular and non-singular matrices
Reversal law for the inverse of a product of two matrices
Use of the inverse of a matrix to find the solution of a system of linear equations
Orthogonal and ur.itary matrices
Partitioning of matrices
Chapter 4: Rank of a matrix.Sub-matrix of a Matrix
Minors of a Matrix
Rank of a matrix
Echelon form of a matrix
Elementary transformations of a matrix
Elementary Matrices
Invariance of rank under elementary transformations
Reduction to normal form
Equivalence of matrices
Row and Column equivalence of matrices
Rank of a product of two matrices
Computation of the inverse of a non-singular
matrix by elementary transformations

Chapter 5: Vector Space of n-tuples
Vectors
Linear dependence and linear independence of vectors
The n-vector space
Sub-space of an n-vector space V
Basis and dimension of a subspace
Row rank of a matrix
Left nullity of a matrix
Column rank of a matrix
Right nullity of a matrix
Equality of row rank, column rank and rank
Rank of a sum
Chapter 6: Linear EquationsHomogeneous linear equations
Fundamental set of solutions
System of linear non homogeneous equations
Condition for consistency
Chapter 7: Eigenvalues and Eigenvectors.Matrix polynominals
Characteristic values and characteristic vectors of a matrix
Characteristic roots and characteristic vectors of a matrix
Cayley-Hamilton theorem
Chapter 8: Eigenvalues and Eigenvectors (Continued)Characteristic subspaces of a matrix
Rank multiplicity Theorem
Minimal polynomial and minimal equation of a matrix
Chapter 9: Orthogonal VectorsInner product of two vectors
Orthogonal vectors
Unitary and orthogonal matrices
Orthogonal group
Chapter 10: Similarity of MatricesSimilarity of matrices
Diagonalizable matrix
Orthogonally similar matrices
Unitarily similar matrices
Normal matrices
Chapter 11: Quadratic formsQuadratic Forms
Linear transformations
Congruence of matrices
Reduction of a real quadratic form
Canonical or Normal form of a real quadratic form
Signature and index of a real quadratic form
Sylvester’s law of intertia
Definite, semi-definite and indefinite real quadratic forms
Hermitian forms 

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