0,3

An n X n nonnegative matrix A is primitive iff every element of A^k is > 0 for some power k. If A is primitive then the power which should have all positive entries is <= n^2 - 2n + 2 (Wielandt).

Sachkov, V. N. and Tarakanov, V. E., Combinatorics of Nonnegative Matrices. Translations of Mathematical Monographs, 213. American Mathematical Society, Providence, RI, 2002.

Wielandt, H. 1950. Unzerlegbare nicht negativen Matrizen, Math. Z. 52, 642-648.

S. J. Leon, Linear Algebra with Applications: THE PERRON-FROBENIUS THEOREM

Index entries for sequences related to binary matrices

For asymptotics see Sachkov and Tarakanov.

Table[ it=Partition[ #, n ]&/@IntegerDigits[ Range[ 0, -1+2^n^2 ], 2, n^2 ]; Count [ it, (q_?MatrixQ) /; (Max@@Table[ Min@@Flatten[ MatrixPower[ q, k ] ], {k, 1, n^2-2n+2} ] )>0 ], {n, 1, 4} ]

Sequence in context: A030247 A139956 A016067 this_sequence A053527 A152504 A035331

Adjacent sequences: A070319 A070320 A070321 this_sequence A070323 A070324 A070325

nonn

N. J. A. Sloane (njas(AT)research.att.com), Aug 22 2003

Wouter Meeussen (wouter.meeussen(AT)pandora.be) computed a(0) through a(4), Aug 22, 2003.

Jack Kennedy (kennedy(AT)oldnews.org) computed a(0) through a(5), Aug 22, 2003.