The following topics are immediate subtopics of Linear Algebra.

Term: Adjoint
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 Definition: The matrix [C_(ji)] = [C_(ij)]^T is called the adjoint (or adjugate) of A and is denoted by adj A. It is the conjugate transpose of A.

Term: Algebraic Multiplicity
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 Definition: The algebraic multiplicity of an eigenvalue is its multiplicity as a root of the characteristic equation.

Term: Augmented Matrix
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 Definition: The augmented matrix is the coefficient matrix augmented by an extra column containing the constant terms.

Term: Back Substitution
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 Definition: The process of solving a linear system of equations that has been transformed into rowechelon form or reduced rowechelon form. The last equation is solved first, then the nexttolast, etc.

Term: Basis
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 Definition: A basis for a subspace S of R^n is a set of vectors in S that 1) spans S and 2) is linearly independent.

Term: Basis Theorem
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 Definition: Let S be a subspace of R^n. Then any two bases for S have the same number of vectors.

Term: Binary Vector
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 Definition: Binary vectors are vectors each of whose components is a 0 or a 1.

Term: Cauchy Schwarz Inequality
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 Definition: For all vectors u and v in R^n, u * v <,= u*v.

Term: Characteristic Equation
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 Definition: The equation det(AcI)=0 is called the characteristic equation of A.

Term: Characteristic Polynomial
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 Definition: The characteristic polynomial of a linear operator T is the polynomial p(t) = det(AtI), where A is the matrix of T with respect to some basis.