1. ## Linear Algebra

If lambda max is the largest eigenvalue of a real symmetric matrix A, show that no diagonal entry of A can be larger than lambda max.

2. ## Re: Linear Algebra

We can show that $\lambda_{\max}=\max_{\lVert x\rVert=1}x^tAx$, using the fact that $A$ is diagonalizable in an orthonormal base.

3. ## Re: Linear Algebra

can u please explain further in detail

4. ## Re: Linear Algebra

First, show the property about $\lambda_{\max}$ I mentioned when $A$ is a diagonal matrix. Jump to the general case using the fact that there exists an orthogonal matrix $P$ and a diagonal matrix $D$ such that $P^tDP=A$.