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The eigenvalues of a 3×3 matrix are the roots of a cubic polynomial which is the characteristic polynomial of the matrix. The characteristic equation of a third-order constant coefficients or Cauchy–Euler (equidimensional variable coefficients) linear differential equation or difference equation is a cubic equation.
Polynomials of degree one, two or three are respectively linear polynomials, quadratic polynomials and cubic polynomials. [8] For higher degrees, the specific names are not commonly used, although quartic polynomial (for degree four) and quintic polynomial (for degree five) are sometimes used. The names for the degrees may be applied to the ...
In mathematics, a cubic function is a function of the form () = + + +, that is, a polynomial function of degree three. In many texts, the coefficients a , b , c , and d are supposed to be real numbers , and the function is considered as a real function that maps real numbers to real numbers or as a complex function that maps complex numbers to ...
The cubic-plus-chain (CPC) [28] [29] [30] equation of state hybridizes the classical cubic equation of state with the SAFT chain term. [21] [22] The addition of the chain term allows the model to be capable of capturing the physics of both short-chain and long-chain non-associating components ranging from alkanes to polymers. The CPC monomer ...
If, on the other hand, f has a non-real root, then K is called a complex cubic field. A cubic field K is called a cyclic cubic field if it contains all three roots of its generating polynomial f. Equivalently, K is a cyclic cubic field if it is a Galois extension of Q, in which case its Galois group over Q is cyclic of order three.
Graph of the polynomial function x 4 + x 3 – x 2 – 7x/4 – 1/2 (in green) together with the graph of its resolvent cubic R 4 (y) (in red). The roots of both polynomials are visible too. In algebra, a resolvent cubic is one of several distinct, although related, cubic polynomials defined from a monic polynomial of degree four:
For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x ...
Cubic crystal system, a crystal system where the unit cell is in the shape of a cube; Cubic function, a polynomial function of degree three; Cubic equation, a polynomial equation (reducible to ax 3 + bx 2 + cx + d = 0) Cubic form, a homogeneous polynomial of degree 3; Cubic graph (mathematics - graph theory), a graph where all vertices have ...