Linear Algebra

# Linear Algebra - Term Definition |v| length of v defined...

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Term: ||v|| Definition: length of v, defined by (v.v)^.5 Term: dimNulA Definition: number of free variables of A Term: geometric multiplicity Definition: the dimension of the eigenspace corresponding to L, ie, dimNul(A - LI) Term: diagonalizable Definition: a matrix is diagonalizable if A is similar to a diagonal matrix, ie if A = PDP-1 where P is invertible and D is a diagonal matrix Term: Chapter 5 Theorem 2: Eigenvectors corresponding to distinct eigenvalues... Definition: are linearly independent

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Term: subspace Definition: a subset of a vector space that:a. has the zero vectorb. is closed under vector additionc. is closed under scalar multiplication Term: rank Definition: the dimension of the column space of A Term: vector space Definition: a non-empty set V of objects, called vectors, on which are defined two operations, called addition and multiplication by scalars, subject to ten axioms. Term: null space Definition: the set of all solutions to the homogeneous equation Ax = 0 Term: Algebraic multiplicity Definition: the number of times Li occurs as a root of the characteristic equation
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