Homework 3. - Purdue College of Engineering
... (Note that when we write, we denote vectors by underlining them (s), but in printed texts it is customary to use boldface letters (s) to denote vectors. Another remark on notation is that a transpose of a column vector is a row vector, thus, an equivalent expression for s is: s = (s(1), s(2), . . . ...
... (Note that when we write, we denote vectors by underlining them (s), but in printed texts it is customary to use boldface letters (s) to denote vectors. Another remark on notation is that a transpose of a column vector is a row vector, thus, an equivalent expression for s is: s = (s(1), s(2), . . . ...
Problem set 3
... (b) Find the change of basis matrix from B to B 0 = [(1, 2)T , (3, 7)T ]. Find it’s inverse (hint: you’ve already done that in this problem set). (c) Use the first two parts to compute the matrix for F with respect to B 0 . (This is not rigged to have a particularly nice answer.) (8) Let F : P≤1 → P ...
... (b) Find the change of basis matrix from B to B 0 = [(1, 2)T , (3, 7)T ]. Find it’s inverse (hint: you’ve already done that in this problem set). (c) Use the first two parts to compute the matrix for F with respect to B 0 . (This is not rigged to have a particularly nice answer.) (8) Let F : P≤1 → 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.