• Shuffle
Toggle On
Toggle Off
• Alphabetize
Toggle On
Toggle Off
• Front First
Toggle On
Toggle Off
• Both Sides
Toggle On
Toggle Off
Toggle On
Toggle Off
Front

### How to study your flashcards.

Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key

Up/Down arrow keys: Flip the card between the front and back.down keyup key

H key: Show hint (3rd side).h key

A key: Read text to speech.a key

Play button

Play button

Progress

1/36

Click to flip

### 36 Cards in this Set

• Front
• Back
 What are 7 properties of invertible matrices? 1. They are square 2. det is not equal to 0, eigenvalues, not equal to 0 3. All orthogonal matrices are invertible 4. columns for a basis of R^n 5. A^T•A is invertible 6. Invertible matrices reduce to identity matrix 7. A and A^-1 have the same eigenvectors If 2 matrices are invertible what form of A has the same eigenvectors as A? A^-1 If A is invertible, is A^3 invertible? Yes If invertible A^2 = A, what does A equal? A=In Do similar matrices have the same eigenvalues? Yes Do simliar matrices have the same algebraic multiplicities? Yes Do A and A^T have the same eigenvectors? No Do A and A^T have the same eigenvalues? No, but they have the same eivenvectors Do similar matrices ahve the same eigenvalues? Yes What is the kernel if rank = m? 0 What is the kernel if image is not equal to n? 0 What is the kernel if det = 0? 0 Are all invertible matrices necessairly similar? No What is the relationship between eivenvectors of symmetric matrices? The eigenvectors are perpendicular For a 2•2 matrix, what conditions have to be met in order to be stable? tr is less than 0 det is greater than 0 For a discrete case, when is the matrix stable? If eigenvalues = p +/- iq and sq. rt.(p^2 + q^2) is less than one The absolute value of each eigenvalue must be less than one What is the least squares solution contained within? Im(A) perpendicular Can rref change determinant? Yes, except when it's not invertible. In that case, the determinant is = to 0 regardless Can rref change eigenvalues and eigenvectors? Yes Can rref change kernel? No Are upper triangular matrices necessarily diagonizable? No What is the relationship between the determinants of simliar matrices? They are the same Can you have the same determinant and different eigenvalues? Yes What is the relationship between the eigenvalues of similar matrices? They are the same. What is a similar matrix? Symmetric with the same eigenvalues If an nxn matrix has a nontrivial kernel, what is guaranteed to be an eigenvalue? 0 Av=0v What does it mean in terms of eigenvalues if nxn has a rank less than n? 0 is an eigenvalue, because kernel is nontrivial If kernel is nontrivial, what is guaranteed to be an eigenvalue? 0 If A is diagonizable, does A^2 have to be diagonizable? No In order to be similar, what conditions have to be met for geometric and algebraic multiplicities? They have to be the same. If A^2 = A, what does it mean in terms of eigenvalues? The eigenvalue is either 0 or 1, because A^2v = lambda^2 v = lambda v = Av Do A^T and A have the same determinant? Yes, as well as the same eigenvalues, but not the same e Do A^T and A have the same eigenvalue? Yes, as well as the same determinant, but not the same e When is te unique squares solution uniqu? When ker is non-trivial, because if v is in ker, then x•nv is a solution What does it mean if a matrix represents a projection onto a line? It's symmetric What are the eigenvalues of a projection? 0 and 1