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Flux balance analysis (FBA) is a mathematical method for simulating the metabolism of cells or entire unicellular organisms, such as E. coli or yeast, using genome-scale reconstructions of metabolic networks. Genome-scale reconstructions describe all the biochemical reactions in an organism based on its entire genome.
The dimension of the column space is called the rank of the matrix and is at most min(m, n). [1] A definition for matrices over a ring is also possible. The row space is defined similarly. The row space and the column space of a matrix A are sometimes denoted as C(A T) and C(A) respectively. [2] This article considers matrices of real numbers
Khatri–Rao product. In mathematics, the Khatri–Rao product or block Kronecker product of two partitioned matrices and is defined as [1][2][3] in which the ij -th block is the mipi × njqj sized Kronecker product of the corresponding blocks of A and B, assuming the number of row and column partitions of both matrices is equal.
Grassmannian. In mathematics, the Grassmannian (named in honour of Hermann Grassmann) is a differentiable manifold that parameterizes the set of all - dimensional linear subspaces of an -dimensional vector space over a field . For example, the Grassmannian is the space of lines through the origin in , so it is the same as the projective space ...
Row and column vectors. In linear algebra, a column vector with elements is an matrix 1 consisting of a single column of entries, for example, Similarly, a row vector is a matrix for some , consisting of a single row of entries, (Throughout this article, boldface is used for both row and column vectors.)
The set of quaternions is a 4-dimensional vector space over the real numbers, with as a basis, by the component-wise addition. and the component-wise scalar multiplication. A multiplicative group structure, called the Hamilton product, denoted by juxtaposition, can be defined on the quaternions in the following way:
The space of Schwartz functions is denoted by (), and its dual ′ is the space of tempered distributions. It is easy to see, by differentiating under the integral and applying the Riemann-Lebesgue lemma, that the Fourier transform of a Schwartz function (defined by the formula Eq.1 ) is again a Schwartz function.
Without proper rendering support, you may see question marks, boxes, or other symbols. Mathematical Alphanumeric Symbols is a Unicode block comprising styled forms of Latin and Greek letters and decimal digits that enable mathematicians to denote different notions with different letter styles. The letters in various fonts often have specific ...