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 A035331 A050819

Adjacent sequences: A070319 A070320 A070321 this_sequence A070323 A070324 A070325

nonn

njas, 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.