- #1

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## Homework Statement

Let {

**u**

_{1},

**u**

_{2},...,

**u**

_{n}} be an orthonormal basis for R

^{n}and let A be a linear combination of the rank 1 matrices

**u**

_{1}

**u**

_{1}

^{T},

**u**

_{2}

**u**

_{2}

^{T},...,

**u**

_{n}

**u**

_{n}

^{T}. If

A = c

_{1}

**u**

_{1}

**u**

_{1}

^{T}+ c

_{2}

**u**

_{2}

**u**

_{2}

^{T}+ ... + c

_{n}

**u**

_{n}

**u**

_{n}

^{T}

show that A is a symmetric matrix with eigenvalues c

_{1}, c

_{2},..., c

_{n}and that

**u**

_{i}is an eigenvector belonging to c

_{i}for each i.

## Homework Equations

No clue...

## The Attempt at a Solution

I'm really stuck with this problem. So I'm really just hoping for a little hint or something.

It SOUNDS easy, but as I said, I have no clue where to start.

Hope you can help.

Regards