\fs Linear vector space, C: . C is closed under some addition and scalar multiplication . a(14) + [B)) = 4/4) + alB) . (c + B)|4) = 014) + 814> . Both operations are commutative and associative . There is a zero element (4) + 10) = (4) VIAjec . There is a unique inverse V [1) ( C that is (1) + | - 1) = 10) . A basis can express any vector in the space VIA) ( C, [1) = >-, Alex) Inner Product: . (A[B) EC . (A|B) = (BIA)' . (4|4) 2 0 with equality