The Gram determinant of vectorsv1,…,vn from an inner product space is the determinant of the n× n matrix with the inner product ofvi andvj as entry in the i th column and j th row; its vanishing is a necessary and sufficient condition for linear dependence.McGraw...
1.Solution of two questions about Gram determinant;关于Gram行列式两个问题的解答 2.The analysis is based on the geometrical interpret ation of the MUSIC method derived from the formula for the Gram determinant and the volume of the polygon.首先,由Gram行列式和超维空间中多面体体积公式,给出常规MUSIC...
However, there is still room to explore the parameterized complexity ofDeterminant Maximizationin therestricted case, in the hope of circumventing the general-case parameterized intractability. Here, we describe three possible scenarios. One can first assume an input matrixto besparse. Of particular in...
For a square matrixA, the determinant of the matrix whose off-diagonal components are equal to those ofA, and whose diagonal components are equal to the difference between those ofAand a parameter λ; it is equal to the characteristic polynomial in λ of the linear transformation represented by...
3. Known classification and enumeration results In 1946 Williamson [25] found the maximal determinants up to n = 7 and showed that there is a unique optimal matrix up to equivalence in each order. I...William P. Orrick, The maximal {-1,1}-determinant of order 15, Metrika 62 (2005),...
This project is created for learning the real world application of linear algebra which contains some core concepts like determinants, matrix, eigen-value, eigen-vector, etc to create a real-world application like steganography, grafh-theory, analysis of spread of disease, image processing, cryptogra...
Consider the matrix(1)N=A+XBY*,where A and B are invertible matrices and X and Y are matrices of conformable size. We assume all matrices are defined over the complex field and (·)* denotes conjugate transpose. The Woodbury matrix identity (Harville [24, p. 427]) represents the ...
Enlargements of cell-to-cell junctions are shown below. Full size image Figure 3 Production of bacterial-associated extracellular matrix. GFP-expressing wild type (WT) M41- and M1-type GAS strains were grown on glass cover slips for 24 h and stained with TRITC-conjugated concanavalin A (ConA...
The isolation of M/NPs usually depends on the sample matrix. For M/NPs in clean aquatic or gas environments, this step can simply be achieved by filtration or centrifugation [218]. Nevertheless, more sophisticated techniques, such as ultracentrifugation [219], ultrafiltration [220], cloud point ...
D. M. Bressoud and J. Propp,The proofs of the alternating sign matrix conjecture, Notices Amer. Math. Soc.46(1999), 637–646. (p. 409) MathSciNetMATHGoogle Scholar T. Brylawski and A. Varchenko,The determinant formula for a matroid bilinear form, Adv. in Math.129(1997), 1–24. ...