cover image: Bulletin of the Calcutta Mathematical Society  April  1917

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20.500.12592/7hxrjv

Bulletin of the Calcutta Mathematical Society April 1917

1917

The degrees of the successive vertical rows are the same in both the matrices A and B. (2) Each of the matrices A and B is vertically primitive when and only when the other is vertically primitive. [...] Then from the equations 97 bi.]=[ctiiai2 a 2] [A] [a; ai2 ai ]=:[bi bi2 bin] K we see that the degree of the i th horizontal row of B cannot exceed the degree of the i th horizontal row of A and that the degree of the *Fth horizontal row of A cannot exceed the degree of the i th horizontal row of B. Therefore the i th horizontal rows of A and B have equal degrees. [...] If c is of standard form then in the theorem (C) the vertical primitive degrees of 613 are the vertical primitive degrees of 4) which are the vertical primitive degrees of the several parts of.13; and in the theorem ( D ) the horizontal primitive degrees of 1 are the horizontal primitive degrees of 0 which are the horizontal primitive degrees of the several parts of 43. [...] 3 there exists a rational integral identity in the variables of the form E [d]: = from which as in the preceding step of the proof we deduce identities of the forms E [8]„i E [81w =[a]r nt The second of these equations shows that all the vertical rows of [81w each of which has degree less than n are connected with the vertical 772 rows of A and therefore with the vertical rows of [b m c [...] From the usual definitions of minimum degrees of connection it follows that in (2) the minimum degrees of liorizoittaconnection of A =1ln are the horizontal primitive degrees of b which are the vertical primL_is tive degrees of B and that in (1) the minimum degrees of vertical r--18 connection of A are the vertical primitive degrees of b which are the un horizontal primitive degrees of
technology medicine science
Pages
60
Published in
India
SARF Document ID
sarf.120023
Segment Pages Author Actions
Frontmatter
i-ii unknown view
Primitive Matrices and the Primitive Degrees of a Matrix Part II
1-32 C.E Cullis view
On the Failure of Poisson’s Equation and of Petrini’s Generalization
33-40 Ganesh Prasad view
On an Interpretation of Fermat’s Law
41-44 C.V Raman view
On the Vibrations of a Membrane Bounded by Two Non-Concentric Circles
45-48 Sudhansukumar Banerji view
Reply to Mr. Raman’s Criticism of Dr. Mallik’s Paper on Fermat’s Law
49-52 D.N Mallik view
Sophie Kovalevsky—The Great Lady Mathematician (1850- 1891)
53-56 Hariprasanna Banerjea view
Review
57-58 Chandi Prasad view

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