Linear Algebra Vocabulary Flashcards

The multiplicity of an eigenvalue as a root of the characteristic equation.

A matrix made up of a coefficient matrix for a linear system and one or more columns to the right.

<p>A polynomial equation in a variable r, created from the coefficients of a homogeneous difference equation.</p> Signup and view all the answers

<p>A variable in a linear system that corresponds to a pivot column in the coefficient matrix.</p> Signup and view all the answers

<p>An indexed set B={v1.....vp} in V such that: B is a linearly independent set and H = span{v1...vp}.</p> Signup and view all the answers

<p>A matrix PC Ax where A is an m x n matrix and x represents any vector in Rn.</p> Signup and view all the answers

<p>A set B that spans H and has the property that if one of the elements is removed from B then the new set does not span H.</p> Signup and view all the answers

<p>Ax = b with b not equal to 0.</p> Signup and view all the answers

<p>It means the matrix is invertible.</p> Signup and view all the answers

<p>A nonzero solution of a homogeneous equation or system of homogeneous equations.</p> Signup and view all the answers

<p>The set of all solutions of the homogeneous equation Ax=0.</p> Signup and view all the answers

<p>x = p + tv.</p> Signup and view all the answers

<p>A nonzero number that is used in a pivot position to create zeros through row operations.</p> Signup and view all the answers

<p>The linear combination of the columns of A using the corresponding entries in x as weights.</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, denoted as rank A.</p> Signup and view all the answers

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

<p>The set Span{v1.....vp}.</p> Signup and view all the answers

<p>A square matrix that has no inverse.</p> Signup and view all the answers

<p>The set of all possible solutions of a linear system; the set is empty when the linear system is inconsistent.</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>Any set {v1....vp} in H such that H = span {v1.....vp}.</p> Signup and view all the answers

<p>The basis E = {e1....en}.</p> Signup and view all the answers

<p>The matrix A such that T(x) = Ax for all x in the domain T.</p> Signup and view all the answers

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

<p>A set of two or more equations with two or more variables.</p> Signup and view all the answers

<p>A rule that assigns to each vector x in Rn a unique vector T(x) in Rm.</p> Signup and view all the answers

<p>An n x m matrix A^T whose columns are the corresponding rows of the m x n matrix A.</p> Signup and view all the answers

<p>A list of numbers or a matrix with only one column.</p> Signup and view all the answers

<p>An equation involving a linear combination of vectors with undetermined weights.</p> Signup and view all the answers

<p>A set of objects, called vectors, on which two operations are defined, adhering to ten axioms.</p> Signup and view all the answers

<p>The subspace {0} consisting of only the zero vector.</p> Signup and view all the answers

<p>The unique vector such that the entries are all zero.</p> Signup and view all the answers