Matrix Groups: Part 3

Based on pages 7 to 9 of my notes. Inner product for n-tuples over K=R,C, H are described using appropriate conjugations. Also, the isometries of these standard inner products naturally give rise to On(K) which produces at once the seemingly distinct matrix groups O(n) over R, U(n) over C and Sp(n) over H; that is orthogonal, unitary and symplectic matrices