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Title      : Math 2.1 Linear Algebra
Subject      : Mathematics
copyright © 2018   : Karnataka State Open University
Author      : KSOU
Publisher      : Karnataka State Open University
Chapters/Pages      : 12/169
Total Price      : Rs.      : 115
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Vector Spaces Total views (900)  
A vector space is a mathematical structure formed by a collection of vectors: objects that may be added together and multiplied ("scaled") by numbers, called scalars in this unit. The operations of vector addition and scalar multiplication have to satisfy certain requirements, called axioms. This unit mainly deals with standard properties of Vectors, Subspaces, Linear combinations and systems of ......
Pages: 18
Price: Rs 0   
Linear Transformation and Matrix Total views (884)  
A linear map, linear mapping, linear transformation, or linear operator (in some contexts also called linear function is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. As a result, it always maps straight lines to straight lines or O. A. Cayley formally introduced m *n matrices in two papers in 1850 and 1858 (the term "matrix" was c ......
Pages: 25
Price: Rs 18.75   
Elementary Matrix Operation, Rank of a Matrix, Matrix Inverse and System of Linear Equation Total views (887)  
In the previous two units, we have learnt about vector space and linear transformations between two vector spaces U(F) and V(F) defined over the same field F In this unit, we shall see that each linear transformation from n-dimensional vector space U(F) to an m-dimensional vector space V(F) corresponds to an m *n matrix over a field F. Here, we see how the matrix representation of a linear transf ......
Pages: 15
Price: Rs 11.25   
Properties of Determinant, Co-factor Expansions and Cramer's Rule Total views (884)  
An exposition of the theory of determinants independent of their relation to the solvability of linear equations was first given by Vandermonde in his "Memoir on elimination theory" of 1772. Laplace extended some of Vandermonde's work in his Researches on the Integral Calculus and the System of the World (1772), showing how to expand II x II determinants by co-factors. The determinant of a square ......
Pages: 12
Price: Rs 9   
Eigen Values and Eigen Vectors, Diagonalizability and Invariant Subspaces Total views (779)  
Eigen vectors are a special set of vectors associated with a linear system of equations (that is a matrix equation) that are sometimes also known as characteristic vectors, proper vectors, or latent vectors. The determination of the eigen vectors and eigen values of a system is extremely important in physics and engineering, where it is equivalent to matrix diagonalization and arises in such commo ......
Pages: 13
Price: Rs 9.75   
Inner Product Space Total views (771)  
Inner product space is a vector space or function space in which an operation for combining two vectors or functions (whose result is called an inner product) is defined and has certain properties.
Pages: 14
Price: Rs 10.5   
The Adjoint, Normal, Self-Adjoint,Unitary and Orthogonal Operators, Orthogonal Projections and the Spectral Theorem Total views (682)  
Adjoints of operators generalize conjugate transposes of square matrices to (possibly) infinite-dimensional situations, The adjoint of an operator A is also sometimes called the Hermitian conjugate (after Charles Hermite) of A, so, most of the results on unitary spaces are identical to the corresponding results on inner product space.
Pages: 16
Price: Rs 12   
Bilinear and Quadratic Forms Total views (688)  
In this unit, we will generalize the notion of linear forms. In fact, we will introduce the notion of a bilinear form on a finite-dimensional vector space. We have studied linear forms on V(F). Here, we will study bilinear forms as mapping from V*V to F, which are linear forms in each variable. Bilinear forms also give rise to quadratic and Hermitian forms.
Pages: 10
Price: Rs 7.5   
The Diagonal and Triangular Form Total views (684)  
If every linear operator is not diagonalizable, even if its characteristic polynomial splits. That purpose of this unit to consider alternative matrix representations for non diagonalizable operators. Such representation is generally, known as canonical forms.
Pages: 14
Price: Rs 10.5   
The Jordan Canonical Form Total views (683)  
The Jordan canonical form describes the structure of an arbitrary linear transformation on a finite-dimensional vector space over an algebraically closed field. Here we study only the most basic concepts of linear algebra, with no reference to determinants or ideals of polynomials.
Pages: 12
Price: Rs 9   
The Minimal Polynomial Total views (681)  
The minimal polynomial deals the distinct eigenvalues and the size of the largest Jordan block corresponding to eigenvalues. In this unit, we study the minimal polynomial, which is played vital role of canonical forms, particularly generalized eigenvalue and eigen vector.
Pages: 9
Price: Rs 6.75   
The Rational Canonical Form Total views (682)  
The generalizations of the eigenvalue and eigen space, this unit deals with a suitable canonical form of a linear operator to this context.
Pages: 11
Price: Rs 8.25   

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