Noun:

सदा एकसां, बेबदलता, अचल,

Adjective:

सदा एकसां, बेबदल,

invariant's Usage Examples:

Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...

respectively: then the result arrived at above from the logarithmic expansion may be written (n)a(n x) = (n)x, exhibiting (n) " as an invariant of the transformation given by the expressions of X1, X2, X3...

When the latter invariant, but not the former, vanishes, the system reduces to a single force.

1 A2B' Where The Denominator Factors Indicate The Forms Themselves, Their Jacobian, The Invariant Of The Quadratic And Their Resultant; Connected, As Shown By The Numerator, By A Syzygy Of Degreesorder (2, 2; 2).

Again, for the cubic, we can find A3(z) - -a6z6 1 -az 3.1 -a 2 z 2.1 -a 3 z 3.1 -a4 where the ground forms are indicated by the denominator factors, viz.: these are the cubic itself of degree order I, 3; the Hessian of degree order 2, 2; the cubi-covariant G of degree order 3, 3, and the quartic invariant of degree order 4, o.

Remark.-The invariant C is a numerical multiple of the resultant of the covariants i and j, and if C = o, p is the common factor of i and j.

This expression of R shows that, as will afterwards appear, the resultant is a simultaneous invariant of the two forms.

F(a ' a ' a, ...a) =r A F(ao, a1, a2,���an), 0 1 2 n the function F(ao, al, a2,...an) is then said to be an invariant of the quantic gud linear transformation.

This arose from the study by Felix Klein and Sophus Lie of a new theory of groups of substitutions; it was shown that there exists an invariant theory connected with every group of linear substitutions.

from the invariant a2 -2a 1 a 3 -2aoa4 of the quartic the diminishing process yields ai-2a 0 a 21 the leading coefficient of the Hessian of the cubic, and the increasing process leads to a3 -2a 2 a 4 +2a i a 5 which only requires the additional term-2aoa 6 to become a seminvariant of the sextic. A more important advantage, springing from the new form of S2, arises from the fact that if x"-aix n- +a2x n-2.

Synonyms:

invariable,

Antonyms:

mutable, variable,