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

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**》BOOK DETAILS**

*(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**

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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.

**BOOK CONTENT **

**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**E**lementary 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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*DOWNLOAD HERE*

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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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**NOTE : –**If you need anything else more like ebooks, video lectures, syllabus etc regarding your Preperation / Examination then do### 》 ALSO READ

*🔥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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