Identifying Eigenvalues
Three different types of eigenvalues a system can have.
What are n real roots, redundant roots, and complex roots?
Name an application problem the difference equation can be used for
What is population dynamics/digital signal processing/economics?
λ2+11λ +24 = 0
What are 3 and 8?
[1 0
0 1]
What is an identity matrix?
Module used to perform linear algebra operations in Python
What is NumPy?
The type of eigenvalues for a symmetric matrix
What is real?
Another name for difference equations is this
What are reccurance relations?
A = [2 0 0
0 4 0
0 0 5]
What are 2, 4, and 5?
[1 2 2
0 5 5
0 0 6]
What is an upper triangular matrix?
Function that forms a matrix in Python
What is np.array()?
The type of eigenvalues from the characteristic equation λ2+2λ +1 = 0
Redundant roots
The difference equation for the change in population (solving for zk)
What is zk=Akz0 ?
Find the eigenvalues for the following:
[-2 0 1
1 1 0
0 0 -2]
What are -2 and 1?
[1 0 0
0 3 0
0 0 4]
What is a diagonal matrix?
(Will also accept what is a symmetric matrix)
Name a way to perform AB
What is A@B?
OR
What is np.matmul(A,B)?
The types of eigenvalues for a skew symmetric matrix
What is 0 or complex?
Eigenvectors are always this, which means they can form a basis for Rn.
What is linearly independent?
Solve for the eigenvalues:
[3 9
−4 −3]
What are ± 3 sqrt(3i) ?
Matrix with the property AT = - A
What is a skew symmetric matrix?
Use Python to find the eigenvalue to the nearest hundredth of the following matrix:
[-3 -2 1
0 2 -1
1 0 1]
What are -3.15, 0.8, and 2.33?
The eignvalues of a triangular matrix
What are the same values as the diagonal?
The form for Az in terms of λ
What is c1λ1x1+ c2λ2x2+ ... + cnλnxn?
Find the eigenvalues:
[5 2 0
2 5 0
-3 4 6]
What are 3,6, and 7?
[1 2 3
2 4 5
3 6 8 ]
What is a square matrix?
Find the eigenvectors for the following using Python (round to nearest hundredth place)
A = [3 −2
4 −1]
What are 1 + i and 2 and 1 - i and 2?
0.41 +/- 0 .41i and 0.82 if not simplified