In summary, the conversation discusses finding the matrix representation of a linear transformation and using it to find the eigenvalues and formula for a given polynomial. The process involves applying the transformation to basis vectors and converting it into B-coordinates. The resulting matrix is ...
not unique,hence classification is discussed for the purpose of loop transformationEfficient algorithms are developed to generate all kinds of linear equations of distance vectors for a given nested loop.The issue of how to obtain a desired transformation matrix from those equations is also addressed....
What is a matrix determinant? A matrix determinant is a value that can be calculated from a square matrix, which represents the scaling factor of the matrix transformation. It is typically denoted by det(A) or |A|. How is the determinant of a matrix calculated?
We investigate two two-sided optimization problems that have their application in atomic chemistry and whose matrix of unknowns $YinR^{ntimes p}$ ($nge p$) lies in the Stiefel manifold. We propose ananalytic optimal solution of the first problem, and show that an optimal solutionof the sec...
This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm
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Motif finding in Assay for Transposase-Accessible Chromatin using sequencing (ATAC-seq) data is essential to reveal the intricacies of transcription factor binding sites (TFBSs) and their pivotal roles in gene regulation. Deep learning technologies inclu
With an integral transformation, the energy eigenvalue problem of a quantum system is converted into the solving of a non-linear Riccati equation. It is easy to find the ground state energy and the corresponding wavefunction. The relation with usual factorization method is discussed. The ground st...
the matrix of first i columns of v . u denotes the unit roundoff, \(u\approx 10^{-16}\) in ieee double precision arithmetic. we write \(x = \theta (y)\) to mean \(x=o(y)\) and \(y=o(x)\) . 2 existing methods for rational interpolation and least-squares fitting rational...
Our algorithm studied here is based on SeDuMi and CVX, and it can be used for linear, nonlinear and generalized linear models. The transformation invariance property and dependence on the covariance matrix of the correlated errors are derived. We also correct the errors in the literature caused ...