qlinear combination: a1x1+a2x2 +…+akxk, xiÎ Fn, aiÎ F
• span{x1,…,xk}:={x= a1x1+…+akxk: aiÎ F}
qx1,…,xkÎ Fn linearly dependent if there exists a1,…,ak Î F not all zero such that a1x1+…+akxk=0; otherwise they are linearly independent.
q{x1,…,xk}Î S is a basis for S if x1,…,xk are
linearly independent and S = span{x1,…,xk}.
q{x1,…,xk} in Fn are mutually orthogonal if xi*xj=0 forall i¹j and orthonormal if xi*xj=dij
q orthogonal complement of a subspace SÌ Fn
q S^:={yÎ Fn : y*x=0 for all xÎ S}