Work in n-dimensional space with basis e1, ... , en. You are given n-1 vectors, the rows of your matrix, by hypothesis linearly independent. The 1-dimensional null space is generated by a vector orthogonal to these. Use the n-dimensional generalization of the cross product. Append to your matrix the row [e1, ... , en]. Now you have an nxn matrix. Calculate its determinant, and express it as A1 e1 + A2 e2 + ... + An en. Then [A1, ... , An] is a basis for the null space. -- Gene
________________________________ From: Scott Fenton <sctfen@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Saturday, July 13, 2013 4:48 PM Subject: [math-fun] Symbolic null space solutions
Hi all,
I'm not sure if Google's and my linear algebra education are failing me, but I've got a matrix problem that I have no idea how to solve. The basics go like this. I've got an n by (n-1) matrix
Q = [ q[1,1] q[1,2] .... q[1,n] ] [ . ] [ . ] [ . ] [ q[n-1,1] .... q[n-1,n] ]
I can guarantee that all (n-1)x(n-1) matrix minors are non-singular. I'm looking for the general solution of this matrix for a proof I'm working on. Any ideas how to go about doing this?
Thanks, Scott _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun