Let v be a non-zero column vector in R^(n)( i.e n维列向量空间） and v ^(T) (
i.e v 的转置）be its transpose.
(a) Show that the n*n matrix A defined by v*v^(T) ( i.e v乘以v的转置） is of
rank one and is a diagonalizable matrix.
(b) If u is a unit vector in R^(n), show that the matrix H=I-2u*u^(T) is an
invertible matrix. Here I is the identity matrix. ( Hint: Note that u^(T)*v
is a scalar for any column vector v. You may show that the null space of H
is trivial)
(c) If v and w are any two nonzero orthogonal vecto
