Homework 1a

Author: Vinay Kumar (@imflash217) | Date: 31/January/2021

Q1

Q1

Given a vector \(v \in R^n\) and square matrices \(A, B \in R^{n\times n}\); show that:

• \(v^T v\) = trace(\(vv^T\))
• trace(AB) = trace(BA)

Q1 Solution

Let \(v = [v_1, v_2, \cdots, v_n]^T\) be a column vector of size \((n,1)\) - [ ] Then, $v^T v = $