Apuleius, l. 30. et Catalect.
"The Anatomy of Melancholy" by Democritus Junior
Verses are distinguished as Catalectic or Acatalectic.
"New Latin Grammar" by Charles E. Bennett
Dactylic, catalectic couplet of the general form: III III III I / III III III I (with rhyme).
"Harvard Psychological Studies, Volume 1" by Various
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Cat is the space of catalectic multi-matrixes (see de ﬁnitions i n 2).
Irreducibility of G-varieties defined by quadrics
The notation PN k≥0 means Pk∈N . A multi-matrix B ∈ CN×N is catalectic if Bi j = bi+ j for some b ∈ C2N .
Irreducibility of G-varieties defined by quadrics
Note that a catalectic multi-matrix B is symmetric, Bt = B.
Irreducibility of G-varieties defined by quadrics
There exist an isomorphism between the projective space of catalectic multi-matrixes, Cat, and the dual of the image of µ : S 2 (CN ) −→ C2N , Cat −→ Pµ(S 2 (CN ))∨ , B → bbt . where b ∈ C2N is a multi-vector that de ﬁnes B and the associated linear fun ctional bbt : C2N → C is bbt ( x) = bt x.
Irreducibility of G-varieties defined by quadrics
The de ﬁnition of a catalectic multi-matrix B implies that there exist a multi-vector b ∈ C2N such that Bi j = bi+ j .
Irreducibility of G-varieties defined by quadrics
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