7. Let H be a Hilbert space with an orthonormal basis {e,..., en}. (a) Show that...

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7. Let H be a Hilbert space with an orthonormal basis {e,..., en}. (a) Show that any x H can be written in a unique form as x = c = (x, ej). => (b) Show that if x=e, and y =de, then " (x, y) = d. j-1 se, and that 7. Let H be a Hilbert space with an orthonormal basis {e,..., en}. (a) Show that any x H can be written in a unique form as x = c = (x, ej). => (b) Show that if x=e, and y =de, then " (x, y) = d. j-1 se, and that