“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:
- Comprehensive coverage of the topic of matrices, including matrix algebra, determinants, inverses, and systems of linear equations.
- Clear explanations of the concepts and theorems, with the use of solved examples.
- Detailed exercises and problems to help students understand and apply the concepts.
- Coverage of both the theoretical and computational aspects of matrices, providing a good balance between theory and practice.
- Use of numerous solved examples, illustrations, and figures to make the subject more understandable.
- A comprehensive introduction to the subject matter and the development of the subject in a logical and structured manner.
- The book is written in a style that is easy to understand and follow.
- The book also includes a number of solved and unsolved problems to help students test their understanding of the material.
- It is likely intended for use in a college-level course on linear algebra or mathematics
- 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
| Author | A. R. Vasishtha & A. K. Vasishtha |
| Publication | Krishna’s Educational Publisher, Since 1942 |
| Total Pages | 384 Pages |
| Language | English |
| Pdf Quality | Good |
| File type |
| NOTE:- If you want anything else like e-books, practice questions, Syllabus, or any exam-related information, kindly let us know in the comment section below. |
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 Matrices | Basic 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: Determinants | Determinants 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 Matrix | Adjoint 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 Equations | Homogeneous 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 Vectors | Inner product of two vectors Orthogonal vectors Unitary and orthogonal matrices Orthogonal group |
| Chapter 10: Similarity of Matrices | Similarity of matrices Diagonalizable matrix Orthogonally similar matrices Unitarily similar matrices Normal matrices |
| Chapter 11: Quadratic forms | Quadratic 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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