MO640 - Exercises - Matrix medians, Zanetti, Biller, and Meidanis 2013

Exercises marked with (*) require further reading/search beyond the suggested texts.

1. Find spaces V_*(.ABC.), V_*(.AB.C.), V_*(.A.BC.), V_*(.AC.B.), V_*(.A.B.C.) for the matrices below.

   A =   1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1

   ,

   B =   1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0

   ,

   C =   0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0

2. Find matrix median approximation M_A for:

   A =   0 1 0 0 1 0 0 0 0 0 0 1 0 0 1 0

   ,

   B =   0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0

   ,

   C =   0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0

   Is it a matrix median?

3. Find matrix median approximations M_A, M_B, M_C for:

   A =   0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1

   ,

   B =   1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1

   ,

   C =   0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1

   Are they matrix medians?

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© 2015 Joao Meidanis