## Viewing Linear Algebra topics

The following topics are immediate sub-topics of Linear Algebra.

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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 row-echelon form or reduced row-echelon form. The last equation is solved first, then the next-to-last, 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(A-cI)=0 is called the characteristic equation of A.
• #### Term: Characteristic Polynomial

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