Homework 4
... 19) Let V and W be G-modules with characters χ, ψ respectively. Show that χ ⋅ ψ (pointwise product) is the character afforded by the tensor product V ⊗ W. 20) (If you have not seen the ring of algebraic integers – we shall only require the result from c) later on) Let R be an integral domain with qu ...
... 19) Let V and W be G-modules with characters χ, ψ respectively. Show that χ ⋅ ψ (pointwise product) is the character afforded by the tensor product V ⊗ W. 20) (If you have not seen the ring of algebraic integers – we shall only require the result from c) later on) Let R be an integral domain with qu ...
Moghadam
... the lowest score of one of the previous exams if it happens to be more. No make-up exams except for the case of documented illness or emergency and, I should be notified before the exam. Quizzes: There will be some quizzes worth 10% of the final grade. No make up quiz. Grading: Based on the total po ...
... the lowest score of one of the previous exams if it happens to be more. No make-up exams except for the case of documented illness or emergency and, I should be notified before the exam. Quizzes: There will be some quizzes worth 10% of the final grade. No make up quiz. Grading: Based on the total po ...
Test 1
... c) Define the magnitude of a vector. d) What does it mean that multiplication of a vector by a number is distributive over addition of vectors? (Use different symbols to distinguish operations on vectors from operations on numbers.) 2. The Cartesian coordinates of a point (scalar components of the p ...
... c) Define the magnitude of a vector. d) What does it mean that multiplication of a vector by a number is distributive over addition of vectors? (Use different symbols to distinguish operations on vectors from operations on numbers.) 2. The Cartesian coordinates of a point (scalar components of the p ...
Linear algebra
Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.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, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models.