Download Matrices by Ar Vasishtha & Ak Vasishtha Krishna publication pdf. Matrices is among one of the popular book krishna series books pdf free download. A lot of post-undergraduates and undergraduates students look for krishna series mathematics book pdf to boost their learning which will help them in various competition exams such as IITJAM, CSIR-NET etc.

## matrices krishna series pdf 2023:

Krishna series matrices pdf is written by Ar Vasishtha who is one of the popular author in field of mathematics and don’t need any introduction along with AR vasishtha, Ak vasishtha also have a major role in making of this book.

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## matrices book by ar vasishtha pdf chapter content:

The krishna series matrices book pdf cntains 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
• 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

• 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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