Homework Statement
Consider the linear system of equations Ax = b b is in the range of A
Given the SVD of a random matrix A; construct a full rank matrix B for which the solution:
x = B^-1*b
is the minimum norm solution.
Also A is rank deficient by a known value and diagonalizable...
Homework Statement
For a system of equations Ax = b
Let dA be a random perturbation of the matrix A
The error in
Which dA fullfills the equality
norm(A^-1 (da) x) = norm(A^-1) norm(dA) norm(x)
(The SVD of A is known)
(b is a known vector)
Homework Equations
The Attempt...
Homework Statement
Given rank(R) and a QR factorization A = QR, what is the rank(A)
Homework Equations
The Attempt at a Solution
I want to know if multiplication by a full rank orthonormal matrix Q and an upper trapezoidal matrix R yields rank(R)=rank(Q*R)=rank(A)
This is...
Homework Statement
Find the oblique projector P so where range(P) = range(U) and range(I-P) = range(W)
Homework Equations
P^2-P = 0
range(I-P) = null(P)
The Attempt at a Solution
It seems that U and W are complementary subspaces. According to...
Homework Statement
S1 is in subspace of C^n. P unique orthogonal projector P : C^n -> S1, and x is in range of C^n. Show that the
minimization problem: y in range of S1 so that:
2norm(x-y) = min 2norm(x-z)
where z in range of S1
and
variational problem: y in range of S1 so that...
Homework Statement
See image. a) and b) have been solved. The problem is c)
Homework Equations
The Attempt at a Solution
I really have no idea where to begin. For the three systems given there are solutions x in range(A) for system 1 and 2 but not for 3. Therefore I have been...