...find. 118. Any function of the coefficients of a quantic is called an invariant, if when the quantic is linearly transformed, the same function of the new coefficients is equal to the old function * The number of terms in the general equation of the n,h degree homogeneous in k variables is . -r3...

...coefficients of a given equation possess this property of invariance ; viz. that when the equation is linearly transformed, the same function of the new coefficients is equal to the given function multiplied by a quantity independent of the coefficients. The result of his investigations...

...find. 122. Any function of the coefficients of a quantic is called an invariant, if, when the quantic is linearly transformed, the same function of the...modulus of transformation; that is to say, when we have $ (a', 6', c', &c.) = Ap<£ (a, J, c, &c.). Such a function is said to be an absolute invariant when...

...Mind, 1 1 04. II. n. In math., a function of the coefficients of a quantie such that, if the quantie is linearly transformed, the same function of the new coefficients is equal to the first function multiplied by some power of the modulus of transformation. -Absolute, differential,...

...n. — Any function of the coefficients of the equation of a curve is called an INVARIANT, if when linearly transformed the same function of the new...to the old function multiplied by some power of the determinant of transformation. DEF. in. — A covariant is a function of both coefficients and variables,...