Publisher's Synopsis
Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, advanced facial recognition algorithms and the social sciences. Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models. Finally, linear algebra is important partly because it is the science of the only types of equations that we know how to solve easily. Fortunately, many non-linear situations can be studied using linear methods. The best-known example of this is calculus, which is entirely about understanding curvy functions and objects using straight, linear approximations to them. Like any good tool, linear algebra can be put to an incredible variety of uses. Linear Algebra- Theorems and Applications contains selected topics in linear algebra, which represent the recent contributions in the most famous and widely problems. It includes a wide range of theorems and applications in different branches of linear algebra, such as linear systems, matrices, operators, inequalities, etc. However, all major topics are also presented in an alternative manner with an emphasis on nonstandard and neat proofs of known theorems. It contributes new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences and provides perspectives on the historical development of matrix theory and linear algebra. It continues to be a definitive resource for researchers, scientists and graduate students. Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, advanced facial recognition algorithms and the social sciences. Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models. Finally, linear algebra is important partly because it is the science of the only types of equations that we know how to solve easily. Fortunately, many non-linear situations can be studied using linear methods. The best-known example of this is calculus, which is entirely about understanding curvy functions and objects using straight, linear approximations to them. Like any good tool, linear algebra can be put to an incredible variety of uses. Linear Algebra- Theorems and Applications contains selected topics in linear algebra, which represent the recent contributions in the most famous and widely problems. It includes a wide range of theorems and applications in different branches of linear algebra, such as linear systems, matrices, operators, inequalities, etc. However, all major topics are also presented in an alternative manner with an emphasis on nonstandard and neat proofs of known theorems. It contributes new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences and provides perspectives on the historical development of matrix theory and linear algebra. It continues to be a definitive resource for researchers, scientists and graduate students. Linear algebra is essential in analysis, applied math, and even in theoretical mathematics. Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations. Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, advanced facial recognition algorithms and the social sciences. Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models. Finally, linear algebra is important partly because it is the science of the only types of equations that we know how to solve easily. Fortunately, many non-linear situations can be studied using linear methods. The best-known example of this is calculus, which is entirely about understanding curvy functions and objects using straight, linear approximations to them. Like any good tool, linear algebra can be put to an incredible variety of uses. Linear Algebra- Theorems and Applications contains selected topics in linear algebra, which represent the recent contributions in the most famous and widely problems. It includes a wide range of theorems and applications in different branches of linear algebra, such as linear systems, matrices, operators, inequalities, etc. However, all major topics are also presented in an alternative manner with an emphasis on nonstandard and neat proofs of known theorems. It contributes new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences and provides perspectives on the historical development of matrix theory and linear algebra. It continues to be a definitive resource for researchers, scientists and graduate students.