STATS 100C: Linear Models
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
STATS 100C: Linear Models
Problem Set 1
Problem 1.1
Consider the matrices
(a) Determine the rank of the two matrices A and B.
(b) Determine the rank of the two matrices AB and BA.
(c) Determine the kernel of A and B.
(d) Find a basis for Im(A) = column space of A.
(e) Express the orthogonal complement of Im(B), that is, Im(B)丄,as the span of a set of vectors.
Problem 1.2
Find the projection of vector x e R3 onto vector a e R3 where
Problem 1.3
Consider the following the matrix:
(a) Find the spectral decomposition of A, that is write A = UAUT where U is orthogonal and A is diagonal.
(b) Use the spectral decomposition, to determine the rank of A.
(c) Is A positive semidefinite (PSD)?
2022-01-12