Linear Algebra Final Exam Flashcards

An indexed set B = {v1,...,vP} in V that is linearly independent and spans H.

<p>The closest point in a given subspace to a given vector.</p> Signup and view all the answers

<p>det(A-λI) = 0</p> Signup and view all the answers

<p>The set R^m that contains the range of T.</p> Signup and view all the answers

<p>The set Col A of all linear combinations of the columns of A.</p> Signup and view all the answers

<p>False</p> Signup and view all the answers

<p>A matrix that can be written in factored form as PDP⁻¹.</p> Signup and view all the answers

<p>A square matrix whose entries not on the main diagonal are all zero.</p> Signup and view all the answers

<p>The number of vectors in a basis for S.</p> Signup and view all the answers

<p>The set of all vectors x for which T(x) is defined.</p> Signup and view all the answers

<p>The set of all solutions of Ax = λx.</p> Signup and view all the answers

<p>A scalar λ such that Ax = λx has a solution for some nonzero vector x.</p> Signup and view all the answers

<p>A nonzero vector x such that Ax = λx for some scalar λ.</p> Signup and view all the answers

<p>An algorithm for producing an orthogonal or orthonormal basis for a subspace.</p> Signup and view all the answers

<p>Ax = 0</p> Signup and view all the answers

<p>The vector T(x) assigned to x by T.</p> Signup and view all the answers

<p>False</p> Signup and view all the answers

<p>A quadratic form Q such that Q(x) assumes both positive and negative values.</p> Signup and view all the answers

<p>A nonzero vector space V that has no finite basis.</p> Signup and view all the answers

<p>AA⁻¹ = A⁻¹A = I</p> Signup and view all the answers

<p>A linear transformation T: R^N →R^N with an inverse function S.</p> Signup and view all the answers

<p>A square matrix that possesses an inverse.</p> Signup and view all the answers

<p>Two vector spaces V and W with a one-to-one linear transformation T mapping V onto W.</p> Signup and view all the answers

<p>A one-to-one linear mapping from one vector space to another.</p> Signup and view all the answers

<p>The set of x in V such that T(x) = 0.</p> Signup and view all the answers

<p>The distance ‖b - Ax∧‖ from b to Ax∧.</p> Signup and view all the answers

<p>A vector x∧ such that ‖b - Ax∧‖ ≤ ‖b - Ax‖ for all x in R^n.</p> Signup and view all the answers

<p>The scalar ‖v‖ = √(v₁² + v₂² + ... + vₙ²).</p> Signup and view all the answers

<p>A sum of scalar multiples of vectors.</p> Signup and view all the answers

<p>False</p> Signup and view all the answers

<p>True</p> Signup and view all the answers

<p>A rule T that assigns a unique vector T(x) in W to each vector x in V, maintaining certain properties.</p> Signup and view all the answers

<p>A quadratic form Q such that Q(x) &lt; 0 for all x ≠ 0.</p> Signup and view all the answers

<p>A function Q defined for x in R^n by Q(x) = x^(T)Ax.</p> Signup and view all the answers

<p>The set of all vectors of the form T(x) for some x in the domain of T.</p> Signup and view all the answers

<p>The dimension of the column space of A.</p> Signup and view all the answers

<p>Two matrices for which there exists a sequence of row operations that transforms one into the other.</p> Signup and view all the answers

<p>The set Row A of all linear combinations of the rows of A.</p> Signup and view all the answers

<p>Matrices A and B such that A = PBP⁻¹ for some invertible matrix P.</p> Signup and view all the answers

<p>The set of all linear combinations of v1,...,vP.</p> Signup and view all the answers

<p>A matrix A such that A^T = A.</p> Signup and view all the answers

<p>A subset H of some vector space V that contains the zero vector and is closed under addition and scalar multiplication.</p> Signup and view all the answers

<p>The sum of the diagonal entries in A.</p> Signup and view all the answers

<p>The only solution of a system.</p> Signup and view all the answers