GLOSSARY OF NEW OR UNUSUAL TERMS, 
546 
Inverse — inverse to a given square matrix is formed by selecting m its turn each component 
of the given matrix, substituting unity in its place, making aU the other components in the same 
line and column therewith zero, and finally writing the value of the determinant corresponding to 
the matrix thus modified in lieu of the seleeted component. If the determinant to the matrix be 
equal to unity, its second inverse, i. e. the inverse to its inverse, will be identical, term for term, 
with the original matrix. 
Jacobian— "The. Jacobian to n homogeneous functions of n variables is the determinant repre- 
sented by the symmetrical collocation in a square of the n differential coefficients of each of the n 
functions. 
Kenotheme.—K finite system of discrete points defined by one or more homogeneous equations 
in number one less than the number of variables contained therein. 
Umitiny Series.-One set of quantities whose extreme values are exterior to the extreme values 
of a second set is set to limit the latter. 
Matrix . — A square or rectangular arrangement of terms in lines and columns. 
Minor Determinant.— Knj determinant retained represented by a square group of terms arbi- 
trarily chosen out of a matrix is a minor determinant thereto. The simple teimis of the matnx are 
the last minors, and of course if the matrix is a square, it will itself in its totality represent a single 
complete determinant. 
Monotheme.- A line, or finite system of lines, defined by one or more homogeneous equations two 
less in number than the numbers of the variables contained therein. 
Order. The orders of a homogeneous function are the linear functions of the variables the least 
in number by aid of which the function admits of being expressed. 
Persymmetrical.—K symmetrical matrix, in which all the terms in the diagonal bands transverse 
to the axis of symmetry are identical, is said to be persymmetrical. Ex. An addition table. 
Quadrinvariant.—Kn invariant of which the terms are quadratic functions of the coefficients of 
the primitive. 
Relation (simple and compound). Vide Substitution^ infra. 
Resultant.— "The resultant of n homogeneous general functions of n variables is that function 
of their coefficients which, equalled to zero, expresses in the simplest terms the condition of the 
possibility of their coexistence. 
Rhizoristic.—A rhizoristic series is a series of disconnected functions which serve to fix the 
number of real roots of a given function lying between any assigned limits. 
Signaletic . — A signaletic or Semaphoretic series is a sequence of disjunctive terms, considered 
solely with reference to the algebraical signs of plus and minus which they respectively carry. 
Singular.-A proper algebraical function of a given degree, n, in one variable in its most general 
form, will, in respect to that variable, be of the «th degree in the denominator and the («-t)th 
dea-i4 in the numerator, and will admit of being represented by a continued algebraical fraction ot 
n terms, all of them linear. _ r r 
But for particular values of, or relations among, the coefficients entering into the given fraction 
this mode of representation fails, and the continued fraction, instead of consisting of linear terms 
