Matrices a.r. Vasishtha (krishna series) PDF Download free 2023

Download Materices by Ar Vasishtha & Ak Vasishtha Krishna publication pdf, Krishna Series books pdf



(Matrices Ar Vasishtha & Ak Vasishtha Krishna  Publication)

Metrices Ar Vasishtha Ak Vasishtha Krishna  Publication pdf Download 

A good book to refer to the matrices problem. Nice method and problems. The way of proof of every theorem, examples and etc., is very good. You can very easily understand all the concepts from this book.
This Book is very beneficial  For those students who are preparing for UPSC, Engineering, SSC, Banking And Other Competitive Examination Etc. Also very helpful  for Graduation level College Students of B.A. and B.Sc. 

This book is best startup for those who are going to give up their career for mathematics.

  • All basic proofs are proved.
  • Almost theory covered.
  • Nearly 300 problems solved.

METRICES Krishna Series PDF by A. K. Vasishtha & A. R.  Vasishtha Download

In this post you can Download this Book  in the Pdf  Format. 

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Matrices Krishna Series Book PDF A R Vasishtha : 

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged / grouped in rows and columns.

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Linear Algebra Ar Vasishtha Krishna publication pdf, Krishna Series books …

Linear algebra is a field of mathematics that is universally agreed to be a prerequisite to a deeper understanding of machine learning. Although linear algebra is a large field with many esoteric theories and findings, the nuts and bolts tools and notations taken from the field are practical for machine learning practitioners. With a solid foundation of what linear algebra is, it is possible to focus on just the good or relevant parts.


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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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METRICES (Krishna Series) Book pdf  for  IIT JAM & other M.Sc Entrances.

Author A. R. Vasishtha & A. K. Vasishtha
Publication Krishna’s Educational Publisher, Since 1942
Total Pages
384 Pages
Language English
Pdf Size ( in MB) 42 MB
File type Pdf
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🔥Modern (Abstract) Algebra Book🔥by A R Vasishtha, FREE PDF DOWNLOAD

It is prepared to keep in mind the students who are currently studying for various Universities UG and PG and I.A.S And P.C.S are preparing for the competition. It is really a very good book for honours and m.Sc maths students. It gives you a depth concepts of   each and  every topic  through  an easy and unique way. Inshort, It is one of the  best book for modern algebra. 

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