Skip to main content

चार महीने का बच्चा कैसे बना अरब़पति

चार महीने का बच्चा कैसे बना अरब़पति? जन्म के सिर्फ चार माह बाद यदि कोई बच्चा अरबपति बन जाए तो इसे उसकी किस्मत ही कहेंगे। भारत के एकाग्रह रोहन मूर्ति नाम के बच्चे की किस्मत कुछ इसी प्रकार चमकी है। देश की दूसरी सबसे बड़ी आइटी कम्पनी इंफोसिस के फाउंडर नारायण मूर्ति ने सोमवार अपने चार महीने के पोते एकाग्रह मूर्ति को 240 करोड़ रूपए के शेयरों की हिस्सेदारी का तोहफा देकर उसे शायद देश का सबसे कम उम्र का अरबपति बना दिया है। BSE की फाइलिंग के अनुसार इंफोसिस में अब एकाग्रह रोहन की 15 लाख शेयरों की हिस्सेदारी हो गई है। इसका मतलब अब एकाग्रह रोहन इंफोसिस का 0.04% का हिस्सेदार है। शेयरों के स्थानान्तरण के बाद नारायण मूर्ति के पास कम्पनी के कुल शेयरों का 0.36% हिस्सा बचा है। जिस समय नारायण मूर्ति द्वारा अपने पोते को शेयर देने की खबर बाई उस समय इंफोसिस के शेयरों में गिरावट देखने को मिल रही थी। एकाग्रह रोहन, नारायण मूर्ति तथा सुधा मूर्ति के बेट रोहन मूर्ति और उनकी पत्नि अर्पणा कृष्णन का बेटा है। आपको यह पता होगा कि नोरायण मूर्ति ने अपनी पत्नि सुधा मूर्ति से 10 हजार रूपए उधार लेकर 1981 में इंफोसिस क
Post a Comment

Algebra | Mathematics | BSc

Algebra

Matrices, Theory of Equation and Group Theory



Authors: Dr. Vimal Saraswat, Dr. Gajendrapal Singh Rathore 

ISBN : 978-93-94954-35-9 

Price: Rs. 385.00

Publisher: Himanshu Publications, Hiran Magri Udaipur; Himanshu Publications Prakash House, Ansari Road, New Delhi

E-mail : info@sacademy.co.in

Phone: +91 9664392614

To buy this book click on Algebra by Saraswat

This book includes the following topics 

Matrix and its Rank

  • Introduction
  • Types of matrices
  • Operation on matrices or matrix algebra
  • Properties of matrix addition
  • Properties of scalar multiplication of matrix
  • Trace of a matrix
  • Multiplication of matrices
  • Properties of matrix multiplication
  • Transpose matrix
  • Symmetric and skew symmetric matrix
  • Orthogonal matrix
  • Conjugate matrix
  • Conjugate transpose matrix or tranjugate matrix
  • Unitary matrix
  • Hermitian and skew-Hermitian matrices
  • Sub matrx of a matrix
  • Determinant of a square matrix
  • Properties of determinant
  • Singular and non-singular matrix
  • Adjoint or adjugate matrix
  • Inverse of a matrix
  • Adjoint method for finding the inverse of a matrix
  • Elementary transformation method for finding the inverse of a matrix
  • Vector
  • Linear combination
  • Linear independent and linear dependent vector
  • Rank of a matrix
  • Column rank and row rank of a matrix
  • Nullity of a matrix
  • Equivalent matrix
  • Normal or canonical form of a matrix

Linear Equations, Eigen Values and Eigen Vectors

  • Introduction
  • System of homogeneous linear equation and their solution
  • System of non-homogeneous linear equations and their solution
    • ramer's rule, Inverse matrix method, Elementary transformation method
  • Condition of consistency
  • Working method for finding the solution of system of non-homogeneous linear equations
  • Triangular or echelon form of a matrix
  • Characteristics equation of a matrix
  • Cayley-Hamilton theorem
  • Application of Cayley-Hamilton's theorem
  • Eigen values and eigen vectors
  • Properties of eigen values of any characteristic equation
  • Nature of characteristic root or eigen values of some special type of matrices

Theory of Equations

  • Introduction
  • Rational integral function or polynomials
  • Equation
  • Roots of an equation
  • सIdentity
  • Properties of equation
  • Relation between roots and coefficients of equation
  • Solution of equation using relations of roots and coefficients
  • Symmetric function of the roots
  • Transformation of equations
    • Equation whose roots are k times the roots of a given equation, Equation whose roots are oppositely signed of a given equation, Equation whose roots are the reciprocals of the roots of a given equation
  • Reciprocal equation
  • Synthesis division
    • To diminish the roots by a given number; To remove a particular terms of an equation

Cubic and Biquadratic Equations

  • Introduction
  • Descarte’s rule of sign
  • Solution of cubic equation by Cardon’s method
  • Solution of general cubic equation by Cardon’s methods
  • Nature of the roots of cubic equations
  • Solution of biquadratic equation by Ferrari’s method
  • Newton’s method of approximation/li>
  • Horner's method

Group

  • Introduction
  • Cartesian product
  • Algebraic structure
  • Binary operation
  • Group
  • Finite and infinite group
  • Groupoid or quasi group
  • Semi-group
  • Monoid
  • Commutative or abelian group
  • Order of a group
  • Modulo operation
  • Uniqueness property in group
  • Properties of inverse in group
  • Cancellation law in group
  • Left and right identity element
  • Left and right inverse
  • Theorems based on semi group
  • Integral power of an element of group
  • Order of an element of a group
  • Klein's 4-group
  • Theorems based on order of element of a group

Subgroup

  • Introduction
  • Subgroup
  • Examples of subgroup
  • Multiplication of complexes of a group
  • Inverse of a complex of a group
  • Necessary and sufficient condition for a subgroup
  • Necessary and sufficient condition for a finite subset to be a subgroup
  • Necessary and sufficient condition for union to be a subgrop
  • Coset
  • Lagrange's theorem
  • Index of subgroup
  • Relation of congruence modulo of a group with respect to a sugroup
  • Euler's ф function
  • Properties of Euler's ф function
  • Euler's theorem
  • Fermat's theorem

Cyclic Group

  • Introduction
  • Cyclic group
  • Theorems based on cyclic group

Normal Subgroup and Quotient Group

  • Introduction
  • Normal subgroup
  • Simple group
  • Theorem based on normal subgroup
  • Quotient group
  • Commutator subgroup

Permutation Group

  • Introduction
  • Permutation
  • Equivalent or equal permutation
  • Identity permutation)/li>
  • Product of permutation
  • Inverse permutation
  • Permutation group
  • Symmetric group
  • Cyclic permutation or cycles and the length of cyclic permutation
  • Inverse of cycle
  • Order of a cycle
  • Disjoint cycles
  • Order of permutation
  • Transposition
  • Even and odd permutation

Group Homomorphism

  • Introduction
  • Homomorphism
  • Types of homomorphism
    • Monomorphism, Epimorphism, Isomorphism, Endomorphism, Automorphism
  • Kernel of homomorphism
  • Theorem based on homomorphism
  • Natural homomorphism
  • Fundamental theorem of homomorphism
  • Three theorems on isomorphism
  • Cayley's theorem
  • Inner automorphism

Centre of group, Normalizer and Class equation

  • Introduction
  • Conjugate elements
  • Conjugate class
  • Self-conjugate element
  • Normalizer of an element
  • Centre of group
Labels:

Comments

Post a Comment

Popular posts from this blog

Electric field due to circular loop of charge | Electromagnetics

Electric field due to circular loop of charge Electric field The space around a charged particle in which another charge experience a force is known as electric field. The source of electric field is either a charge or a time varying magnetic field. If the value of electric field does not change with time, then it will be uniform electric field, otherwise it will be non-uniform electric field. Electric field due to circular loop of charge If λ is linear charge density, then the charge on d l dq = λ d l      ⇒     dq = (q / 2πa) d l Electric field at P due to charge dq Special cases When P lies at the centre of the loop i. e., r = 0, then E = 0 When P lies very far from the centre of the loop i. e., r >> a, then E = kq / r 2 In this case circular loop behaves as a point charge. To know more about this topic please click on the link  https://youtu.be/54MIe0Ow43w   or   https://youtu.be/9bR1LfbVrGw
Post a Comment
Read more

Constraints | Classification and Properties of constraints | Classical mechanics

Constraints and its classification Constraints force Constraints are restrictions that limit the motion of the particles of a system. Physically constrained motion is realized by the forces which arise when the object in motion is in contact with the constraining surfaces or curves. These forces are called constraint forces. Properties of constraints force They are elastic in nature and appear at the surface of contact. They are so strong that they barely allow the body under consideration to deviate even slightly from a prescribed path or surface. This prescribed path or surface is called a constraint. The effect of constraint force is to keep the constraint relations satisfied. Classification of constraints           Scleronomic and Rheonomic This classification is based on time. The constraints are said to be scleronomic constraints, if the constraint relations do not explicitly depend on time. But if the constraint relations explicitly depend on ti
Post a Comment
Read more

Advantage and Disadvantage of Power Electronics

Advantage and Disadvantage of Power Electronics Advantage of Power electronics Power electronics is used in space shuttle power supplies Since there is very low loss in power electronic devices so its efficiency is very high. Power electronic converter systems are highly reliable. Since there is no moving parts in power electronic systems so it has long life and also its maintenance cost is very less. The power electronic systems has fast dynamic response in comparison to electromechanical converter systems. Since the power electronic system has small size and also it has less weight so they occupy less floor space and hence their installation cost is also less. Now these days power equipments are being mostly used, so power semiconductor devices are being produced on a large scale, resulting in lower cost of converter equipment. Power electronics are used in computer and office equipments. It is used in uninterruptible power supplies. Power
Post a Comment
Read more

Adesterra