There are four kinds of scalars in the n-dimensional pseudo-Euclidean geometry of index one. In this note, we determine all scalars as concomitants of a system of m ≤ n linearly independent contravariant vectors of two so far missing types. The problem is resolved by finding the general solution of the functional equation F(Au 1 , Au 2 , . . . , Au m ) = ϕ (A) · F(u 1 , u 2 , . . . , u m ) using two homomorphisms ϕ from a group G into the group of real numbers R0 = (R \ {0} , ·).
In this note, there are determined all biscalars of a system of s ≤ n linearly independent contravariant vectors in n-dimensional pseudo-Euclidean geometry of index one. The problem is resolved by finding a general solution of the functional equation F(Au1 , Au2 , . . . , Aus ) = (sign(det A))F(u1 , u2 ,...,us ) for an arbitrary pseudo-orthogonal matrix A of index one and the given vectors u1 , u2 ,...,us .
This paper deals with the reconstruction of the now longer preserved gallery of coats of arms at Roupov Castle (District of Klatovy, Western Bohemia) based on manuscripts XVII.A.8 and XVII. E. 28 a from the Czech National Library. Information from individual manuscripts was combined to form an image of probably the largest Czech family coat of arms gallery at the end of the 16th century containing a collection of coats of arms from 270 noblemen and noblewomen. The gallery probands are Jan Nezdický of Roupov († before 1607) and his two wives – Dorota Bezdružická of Kolovraty and Benigna of Švamberk. The paper draws attention to the utilization of hitherto neglected manuscript sources for research into displays of self-awareness among the privileged classes and it attempts to show the way in which the nobility used genealogical and heraldic means for representative purposes. Not least, these manuscripts are often the only source of information on genealogical and heraldic artefacts which are no longer in existence.