Linear Algebra a.r. Vasishtha (Krishna Series) PDF Download 2022 Free

linear algebra a.r. vasishtha (krishna series) pdf download free

Download linear algebra a.r. vasishtha (krishna series) pdf free



(Linear Algebra Ar Vasishtha Krishna  Publication)

Linear Algebra Ar Vasishtha Krishna  Publication pdf Download 

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.

In this tutorial, you will discover what exactly linear algebra is from a machine learning perspective.

After completing this tutorial, you will know:

  • Linear algebra is the mathematics of data.
  • Linear algebra has had a marked impact on the field of statistics.
  • Linear algebra underlies many practical mathematical tools, such as Fourier series and computer graphics
  • Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics

This Book is very useful  For UPSC, Graduation level College Students BSC all sem ( 1st, 2nd, 3rd year ), BA (1st, 2nd, 3rd, 4th, 5th, 6th semester ), Engineering, SSC, Banking And Other Competitive Examination Etc.

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

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Linear Algebra Krishna Series PDF by J.N Sharma & A.R Vasishtha Download

In this post you can Download this Book  in the Pdf  Format. 
If You are Facing Any type of  Problem in Downloading 📥 The Book Or The Link Has Been Broken, Then Please Feel Free 😋To Comment Us below in the comment section.



Chapter 01. Vector Spaces

  • Binary operation on a set
  • Group. Definition
  • Field. Definition
  • Vector space. Definition
  • General properties of vector spaces
  • Vector subspaces
  • Algebra of subspaces
  • Linear combination of vectors. Linear span
  • Linear sum of two subspaces
  • Linear dependence and linear independence of vectors
  • Basis of a vector space
  • Finite-dimensional vector spaces
  • Dimension of a vector space
  • Dimension of a subspace
  • Homomorphism of vector spaces or Linear Transformations
  • Isomorphism of vector spaces
  • Quotient spaces
  • Direct sum of spaces
  • Disjoint subspaces
  • Complementary subspaces
  • Coordinates


Chapter 02. Linear Transformations

  • Linear Transformations
  • Linear operator
  • Range and null space of a linear transformation
  • Rank and nullity of a linear transformation
  • Linear transformations as vectors
  • Product of linear transformations
  • Algebra or Linear algebra
  • Invertible linear transformations
  • Singular and non-singular transformation
  • Matrices. Definition
  • Representation of transformations by matrices
  • Similarity
  • Determinant of Linear transformation
  • Trace of a matrix
  • Trace of a linear transformation
  • Linear functionals
  • Dual spaces
  • Dual bases
  • Reflexivity
  • Annihilators
  • Invariant direct sum decompositions
  • Reducibility
  • Projections
  • The adjoint or transpose of a linear transformation
  • Sylvestor’s law of nullity
  • Characteristic values and characteristic vectors or proper vectors
  • The Cayley-Hamilton theorem
  • Diagonalizable operators
  • Minimal polynomial and minimal equation

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Chapter 03. Inner Product Spaces

  • Inner Product spaces. Definition
  • Euclidean and unitary spaces
  • Norm or length of a vectorSchwarz’s inequality
  • Orthogonality
  • Orthonormal set
  • Complete orthonormal set
  • Gram-Schmidt orthogonalization process
  • Projection theorem
  • Linear functionals and adjoints
  • Self-adjoint transformations
  • Positive operators
  • Non-negative operator
  • Positive matrix
  • Unitary operators
  • Normal operators
  • Characterization of Spectra
  • Perpendicular projections
  • Spectral theorem


Chapter 04. Bilinear Forms

  • Bilinear Forms. Definitions
  • Bilinear forms as vectors
  • Matrix of a bilinear form
  • Symmetric bilinear forms
  • Skew-Symmetric bilinear forms
  • Groups preserving bilinear forms
Model Papers





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


Author A. R. Vasishtha & J. N. Sharma
Publication Krishna’s Educational Publisher, Since 1942
Total Pages
417 Pages
Language English
Pdf Size ( in MB) 30 MB
File type Pdf

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NOTE : – If you need anything else more like ebooks, video lectures, syllabus  etc regarding  your Preperation / Examination  then do  📌mention in the Comment Section below. 



  • Samvedna Publication , Vector Calculus, Linear Algebra and Real Analysis book for IIT JAM – MATHS : – DOWNLOAD HERE
  • MCQ Mathematics Practice Book pdf for  IIT JAM, NET , SET , GATE etc. : –  DOWNLOAD HERE
  • Introduction to Real Analysis by SADHAN KUMAR MAPA (S. K. MAPA), BOOK PDF : – DOWNLOAD HERE 
  • S. CHAND BOOK , Elements of Real Analysis by SHANTI NARAYAN and Dr. M. D. RAISINGHANIA,  PDF  : – DOWNLOAD HERE
  • HCU Mathematics M.Sc Entrance PREVIOUS YEAR QUESTION PAPERS (2010 – 2020) : – DOWNLOAD HERE

》 ALSO Read


Modern Algebra by 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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