NullSpaceExample-2003

# NullSpaceExample-2003 - AEB 6533 Some Examples of...

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AEB 6533 Some Examples of Nullspaces I. Starting with a simple 2*3 example, assume that we have the matrix equation 1 2 3 11 1 5 011 6 x Ax b x x   =⇒ =  A. Note that by row operations the A matrix can be transformed to 111 11 102 01 0 1 1 = B. This expression implies the following homogeneous relationships: 13 23 20 0 xx + = + = 1. Setting 3 1 x = yields 1 2 2 1 x x = − = − 2. Or in vector form: 2 1 1 z = C. Next we confirm that z is the nullspace. We do this by confirming that both vectors of the A matrix are orthogonal to the nullspace: () 2 2 1 1 0 1 2 011 1 0110 1 −= −++= −=−+= D. Implications of the nullspace: 1. Start by defining a feasible solution: 51 1 1 1 1 5 1 0 2 1 1 60 1 0 1 1 6 0 1 1 6 11 1 1 1 6 0 5 6 6 0 Ax     =         −− + ⇒= = + 2. Next, we would like to generate another feasible point based on this solution and the nullspace matrix:

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AEB 6533 – Static and Dynamic Optimization Nullspace Examples Professor Charles B. Moss 2 () 1 * 2 3 11 2 61 01 x x xZ p x p x     =+ = +
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## This note was uploaded on 11/08/2011 for the course AEB 6533 taught by Professor Moss during the Fall '08 term at University of Florida.

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NullSpaceExample-2003 - AEB 6533 Some Examples of...

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