Thread: 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.

We can show that , using the fact that is diagonalizable in an orthonormal base.

can u please explain further in detail

First, show the property about I mentioned when is a diagonal matrix. Jump to the general case using the fact that there exists an orthogonal matrix and a diagonal matrix such that .