MathDB
tranpose, 5x10 matrices

Source: VTRMC 2005 P7

June 10, 2021
matrixlinear algebra

Problem Statement

Let AA be a 5×105\times10 matrix with real entries, and let ATA^{\text T} denote its transpose. Suppose every 5×15\times1 matrix with real entries can be written in the form AuA\mathbf u where u\mathbf u is a 10×110\times1 matrix with real entries. Prove that every 5×15\times1 matrix with real entries can be written in the form AATvAA^{\text T}\mathbf v where v\mathbf v is a 5×15\times1 matrix with real entries.
Back to ProblemsView on AoPS