Get inspired by the success stories of our students in IIT JAM MS, ISI  MStat, CMI MSc DS.  Learn More

# Tracing the Trace | ISI MStat 2016 PSB Problem 3 This ISI MStat 2016 problem is an application of the ideas of tracing the trace and Eigen values of a matrix and using a cute sum of squares identity.

## Problem- Tracing the Trace

Suppose A is an real symmetric matrix such that . Show that all the eigenvalues of A are equal to 1.

This problem is from ISI MStat 2016 PSB ( Problem #3)

### Prerequisites

• Trace of a Matrix
• Eigen values of w.r.t to the eigen values of .
• Sum of Squares .

## Solution .

Since, A is a real symmetric matrix, then all the eigen values of the matrix A are real say { }.      .

This ISI MStat 2016 problem is an application of the ideas of tracing the trace and Eigen values of a matrix and using a cute sum of squares identity.

## Problem- Tracing the Trace

Suppose A is an real symmetric matrix such that . Show that all the eigenvalues of A are equal to 1.

This problem is from ISI MStat 2016 PSB ( Problem #3)

### Prerequisites

• Trace of a Matrix
• Eigen values of w.r.t to the eigen values of .
• Sum of Squares .

## Solution .

Since, A is a real symmetric matrix, then all the eigen values of the matrix A are real say { }.      .

This site uses Akismet to reduce spam. Learn how your comment data is processed.

### Knowledge Partner  