Description
1. Let A ∈ F
m×n
, with F = R or C, prove that range(A) is orthogonal to
null(A∗
), i.e., any arbitrary vector in range(A) is orthogonal to an arbitrary
vector in null(A∗
).
2. Use Gram-Schmidt method to find a QR factorization of the matrix
A =
Ñ
1 2 1
3 −1 1
1 1 2é
.
3. Consider a matrix A ∈ F
m×n with m ≥ n and all columns being orthogonal
but not of unit length, what should its reduced QR decomposition look like?
