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The all-ones matrix arises in the mathematical field of combinatorics, particularly involving the application of algebraic methods to graph theory.For example, if A is the adjacency matrix of an n-vertex undirected graph G, and J is the all-ones matrix of the same dimension, then G is a regular graph if and only if AJ = JA. [7]
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Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice. An investor must choose how much to consume and must allocate their wealth between stocks and a risk-free asset so as to maximize expected utility .
where v 1, v 2, ..., v k are in S, and a 1, a 2, ..., a k are in F form a linear subspace called the span of S. The span of S is also the intersection of all linear subspaces containing S. In other words, it is the smallest (for the inclusion relation) linear subspace containing S. A set of vectors is linearly independent if none is in the span ...
The conjugate transpose of a matrix with real entries reduces to the transpose of , as the conjugate of a real number is the number itself. The conjugate transpose can be motivated by noting that complex numbers can be usefully represented by 2 × 2 {\displaystyle 2\times 2} real matrices, obeying matrix addition and multiplication: a + i b ≡ ...
For example, a 2,1 represents the element at the second row and first column of the matrix. In mathematics, a matrix (pl.: matrices) is a rectangular array or table of numbers, symbols, or expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object.
Then a portfolio () = (in physical units, i.e. the number of each stock) is self-financing (with trading on a finite set of times only) if for all t ∈ { 0 , 1 , … , T } {\displaystyle t\in \{0,1,\dots ,T\}} we have that H t − H t − 1 ∈ − K t P − a . s . {\displaystyle H_{t}-H_{t-1}\in -K_{t}\;P-a.s.} with the convention that H − ...
1 for 10 pages; 2 for 20 pages; 4 for 40 pages; 6 for 60 pages; 8 for 80 pages; The third numeral stands for the ruling: 0 for blank exercise book; 1 for lined paper—lines at 20 mm; 2 for lined paper—lines at 16 mm; 3 for lined paper—lines at 12 mm; 4 for lined paper—lines at 8 mm; 5 for squared paper—squares are 5 x 5 mm