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Flashcards in Matrices 1 Deck (10)
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1

when does a sqaure matrix have an inverse?

if the determinant of that matrix is non zero

2

how is the inverse of a matrix defined?

A^-1*A=I, where I is the identity matrix

3

what is the transpose of a matrix?

matrix where rows are columns of the original

4

what is a matrix if its transpose is equal to the original?

symmetric and sqaure

5

what is an eigenvalue and eigenvector?

an eigenvector v and a eigenvector lambda obeys the eqn Av=lambda*v

6

how do you find the eigenvalues?

det(A-lambda*I)=0

7

properties of eigenvalues

eigenvalues of A inverse are the inverse of the eigenvalues of A

eigenvalues of A^2 are the square of the eigenvalues of A

eigenvalues of A and A transpose are the same, but not the same eigenvectors

8

what is the trace of a matrix?

refers to the sum of the diagonal entries of that matrix

9

how to check if eigenvalues are correct?

compare the sum to the trace, should be equal

10

what is a vector norm??

a measure of the magnitude of the vector