Re: tricky matrix problem

["Richard M. Heiberger" <rmh@temple.edu>]

Let's rewrite this in matrix notation.

Let K_i be the matrix that is the i^\th layer of your array K.

Let I_i be the indicator matrix which is 1 in the {i,i} position
and 0 elsewhere.  

Let L_i = (K_i - I_i).

Let x be the vector (x_1, ..., x_n).

Then your problem translates to

x'(I_i)x = x'(K_i)x

Therefore

0 = x'(K_i - I_i)x = x'(L_i)x  for all i.

In words, you have a set of n matrices L_i, each of which is zeroed by
the same single vector x.

What is the story of these matrices?  An arbitrary set of n matrices
is unlikely to have that property.


Rich