Suppose B is a (2x2) matrix such that B2 = I . Show
that the determinant I B I is either +1 or -1. [Hint: A2stands for the matrix product AA. I is the (2x2) identity matrix. A
fact: For any two matrices E and F, I EF I = I E I I F I ]
Hessian Matrix Determinant and Convex/Concave
I have a function which has a Hessian Matrix of:
-2
0
0
0
-16
10
0
10
-4
Can anyone explain why this is neither a positive nor a negative
definite?
And could you please explain 2*2 and 3*3 Hessian's rule of
determining positive/negative definite? Thank you.
Matlab
You will write a function to calculate the determinant of a
matrix. It should work for any size matrix. Remember that the
determinant can be calculated by multiplying the diagonal elements
of an upper right triangular matrix. Your function will take a
matrix passed to it and put it in upper right triangular form. You
will work down the diagonal beginning at row 1 column 1, then row 2
column 2, etc. Note that the row and column numbers...
The determinant of a matrix is the product of its eigenvalues.
Can you prove this when A is diagonalizable? How about if A is 2 x
2, and may or may not be diagonalizable? (Hint: What's the constant
term in the characteristic polynomial>
Diagonalize the matrix (That is, find a diagonal matrix D and an
invertible matrix P such that
A=PDP−1.
(Do not find the inverse of P). Describe all eigenspaces of A
and state the geometric and algebraic multiplicity of each
eigenvalue.
A=
-1
3
0
-4
6
0
0
0
1