Question: minor

Answer: n

(n-1) matrix Aij you get by deleting the 11th row and the jth columns from A.

Question: cofactor

Answer: A is the Cij = (-1) ^i+j detAij

Question: determinant

Answer: of an n n matrix A can be calculated using cofactor

expansion along any row or column:

square matrices

Question: determinant properties

Answer: det(In) = 1

If we do a row replacement on a matrix (add a multiple of one row to another),

the determinant does not change.

If we swap two rows of a matrix, the determinant scales by -1.

If we scale a row of a matrix by k, the determinant scales by k

Question: Eigenvector

Answer: of A is a nonzero vector v in Rn such that Av = v, for some in

R. In other words, Av is a multiple of v

Question: eigenvalue

Answer: of A is a number in R such that the equation Av = v has a

nontrivial solution.

Eigenvectors with distinct eigenvalues are linearly independent.

Question: Eigenspace

Answer: of A is the set of all eigenvectors of A with eigenvalue , plus the zero vector

Question: characteristic polynomial

Answer: of A is f () = det(A- lambdaI).

Question: characteristic equation

Answer: f () = det(A I) = 0.

Question: algebraic multiplicity

Answer: of an eigenvalue is its multiplicity as a root of

the characteristic polynomial.

GM must be larger than this multiplicity for the matrix to span R^n