qlinear transformation A: Fn ® Fm .
q kernel or null space: KerA=N(A):={xÎ Fn : Ax=0}
q image or range of A: ImA=R(A):={yÎ Fm : y=Ax, xÎ Fn}
qLet ai, i =1,2,…, n denote the columns of a matrix AÎ Fm´n. Then
q Im A=span{a1, a2, …, an}.
qThe rank
of a
matrix A is defined by rank(A) = dim(ImA).
q rank(A) = rank(A*).
q AÎ Fm´n is full row rank if m £ n and rank(A) = m.
q A is full column rank if n £ m and rank(A) = n.
qunitary matrix U*U = I = UU*.
q Let D Î Fn´k (n < k) be such that D*D = I. Then there exists a
matrix D^ Î Fn´(n-k) such that [D D^] is a unitary matrix.