# Least squares estimation with quadratic constraints (M*M = 0)

1. Jan 30, 2012

### Michael02

Hello there,

currently I am trying to solve a least squares problem of the following form:

$min_{M}$ ||Y - M*X||$^2$

where M is a 3x3 matrix and Y and X are 3xN matrices. However, the matrix M is of a special form. It is a rank 1 matrix which satisfies M*M = 0$_{3x3}$ and the trace of M is zero, too.

Enforcing that the trace is zero seems rather easy, since it is a linear constraint. But I have no idea how to enforce M*M = 0$_{3x3}$, as it includes multiple quadratic constraints.

Does anyone have an idea how to solve this problem?