Remarkable.
I am not sure, but in your matrices terms containing square roots appear.
In[33]:= Take[#, 10] & /@ Take[bMatrix[91], 3]
Out[33]= {{91/555, 0, Sqrt[91/181]/555, 0, 0, 0, 0, 0, 0, 0}, {0, 88/555, 0, Sqrt[6/905]/37, 0, 0, 0, 0, 0, 0},
{Sqrt[91/181]/555, 0,15391/100455, 0, (2 Sqrt[537/5])/6697, 0, 0, 0, 0, 0}}
And this in case of n = 91 may give rise to rather lengthy (exact Integer Arithmetic) simplification procedures. Try it with machine precision reals:
While
bRank[91]
doesn't com back in a reasonable amount of time (you say it "hangs")
bRank[91.]
does. As well as
In[28]:= {#, bRank[#]} & /@ N[Range[88, 93]]
Out[28]= {{88., 176}, {89., 178}, {90., 180}, {91., 182}, {92.,184}, {93., 186}}
Furthermore it seems that the rank of bMatrix[ L ] is 2 L
In[32]:= {#, bRank[#]} & /@ Range[15]
Out[32]= {{1, 2}, {2, 4}, {3, 6}, {4, 8}, {5, 10}, {6, 12}, {7,14}, {8, 16}, {9, 18}, {10, 20}, {11, 22}, {12, 24}, {13, 26}, {14, 28}, {15, 30}}
Perhaps there is a proof for this?