Seminar on Linear Algebra Friday,18 November 2022 at 3.30 pm Venue: Ramanujan Hall Speaker: Rajesh Sharma, Himachal Pradesh University, Shimla Title: On some inequalities related to the Cauchy-Schwarz inequality in matrix algebra Abstract: We focus on the non-commutative versions of some inequalities related to the Cauchy-Schwarz inequality in matrix algebra. We discuss some inequalities involving positive unital linear maps on matrix algebra and demonstrate how positive linear maps can be used to obtain bounds for the spreads of matrices. The particular cases provide inequalities of statistical interest involving moments of discrete and continuous random variables.