Chapter 6, Problem 3SE

Let {v1, …, v_p} be an orthonormal set in ℝⁿ. Verify the following inequality, called Bessel’s inequality, which is true for each x in ℝⁿ:

${\Vert x\Vert }^2\ge {\left|x\cdot v_1\right|}^2+{\left|x\cdot v_2\right|}^2+\cdots +{\left|x\cdot v_p\right|}^2$