Inner product of rank 2 tensor and a vector

[abluphoton]

I been reading some material that lead me to understand that it takes an inner product of a dyad and a vector to obtain another vector at an angle to the initial one... cross product among two vectors would be an option only if we are willing to settle to a right angle.
After few days i countered a situation where i see an inner product of a vector and a dyad resulting in a vector of different magnitude but same direction as the earlier one. i mean to say
[ A*v = η.v ]
A= a random dyad
v= a vector
η= a scalar.

now the question is, what is the condition for such an interaction ?? what should be the property of such a tensor ?!

 

[jedishrfu]

look at a 2D version of a matrix and a vector say M x V = n x V

M x V = results in:

n*vx=m11*vx + m12*vy

and

n*vy = m21*vx + m22*vy

so what could you set the m values to make the two equations true?