Matrices 1

Question 1

when does a sqaure matrix have an inverse?

Answer 1

if the determinant of that matrix is non zero

Question 2

how is the inverse of a matrix defined?

Answer 2

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

Question 3

what is the transpose of a matrix?

Answer 3

matrix where rows are columns of the original

Question 4

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

Answer 4

symmetric and sqaure

Question 5

what is an eigenvalue and eigenvector?

Answer 5

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

Question 6

how do you find the eigenvalues?

Answer 6

det(A-lambda*I)=0

Question 7

properties of eigenvalues

Answer 7

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

Question 8

what is the trace of a matrix?

Answer 8

refers to the sum of the diagonal entries of that matrix

Question 9

how to check if eigenvalues are correct?

Answer 9

compare the sum to the trace, should be equal

Question 10

what is a vector norm??

Answer 10

a measure of the magnitude of the vector