UCSD ECE 269 Handout # 13

(a) Since A is full-rank and fat, Ax = b has at least one solution. From Problem 4 in HW#4, we know that since C is full-rank and tall, 〈x, y〉C := (Cx) TCy defines a valid inner product. So the problem reduces to one of finding the least-norm solution to Ax = b w.r.t. this inner product. Clearly, the required solution will be found by projecting the zero vector on the affine subspace defined by Ax = b, and this projection should be with respect to the inner product 〈·, ·〉C . Therefore, letting x̃ be the required solution, we must have Ax̃ = b,