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Romania District Olympiad 2003 - Grade XI

Source:

March 18, 2011
linear algebramatrixlinear algebra unsolved

Problem Statement

a)Prove that any matrix A∈M4(C)A\in \mathcal{M}_4(\mathbb{C}) can be written as a sum of four matrices B1,B2,B3,B4∈M4(C)B_1,B_2,B_3,B_4\in \mathcal{M}_4(\mathbb{C}) with the rank equal to 11. b)I4I_4 can't be written as a sum of less than four matrices with the rank equal to 11.
Manuela Prajea & Ion Savu
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