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This definition proceeds by establishing the characteristic polynomial independently of the determinant, and defining the determinant as the lowest order term of this polynomial. This general definition recovers the determinant for the matrix algebra A = Mat n × n ( F ) {\displaystyle A=\operatorname {Mat} _{n\times n}(F)} , but also ...
In mathematics, the Wronskian of n differentiable functions is the determinant formed with the functions and their derivatives up to order n – 1.It was introduced in 1812 by the Polish mathematician Józef Wroński, and is used in the study of differential equations, where it can sometimes show the linear independence of a set of solutions.
In vector calculus, the Jacobian matrix (/ dʒ ə ˈ k oʊ b i ə n /, [1] [2] [3] / dʒ ɪ-, j ɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives.
Some philosophers have maintained that the entire universe is a single determinate system, while others identify more limited determinate systems. Another common debate topic is whether determinism and free will can coexist; compatibilism and incompatibilism represent the opposing sides of this debate.
Determinate, or bush, types bear a full crop all at once and top off at a specific height; they are often good choices for container growing. Determinate types are preferred by commercial growers who wish to harvest a whole field at one time, or home growers interested in canning .
Determinate cleavage (also called mosaic cleavage) is in most protostomes. It results in the developmental fate of the cells being set early in the embryo development . Each blastomere produced by early embryonic cleavage does not have the capacity to develop into a complete embryo .
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In functional analysis, a branch of mathematics, it is sometimes possible to generalize the notion of the determinant of a square matrix of finite order (representing a linear transformation from a finite-dimensional vector space to itself) to the infinite-dimensional case of a linear operator S mapping a function space V to itself.