Indeed, the columns of unitary matrices are unit vectors, so that Un is bounded. On the other hand, Un is defined by an equation U*U = In, where the map UU*U is continuous; hence Un is closed. By the same arguments, On is compact. Polar decomposition is a fundamental tool in the...
By a generalized polar decomposition of an m×n matrix A, it is meant that A can bedecomposed as A=QH, where Q is an m×n subunitary matrix, and H is a Hermite positivesemidefinite matrix. In this paper, the uniqueness theorem of generalized polar decomp
1) polar decomposition 极式分解2) polar decomposition 极分解 1. Focus matrix is constructed by polar decomposition of location matrix and transforms signal sub space at different frequency bins to signal sub space at focusing frequency bin. 通过对方向矩阵进行极分解构造聚焦矩阵,把各个窄带频率处的...
Polar decomposition of 3 x 3 Mueller matrix: a tool for quantitative tissue polarimetry. The polarization properties of any medium are completely described by the sixteen element Mueller matrix that relates the polarization parameters of the li... MK Swami,S Manhas,P Buddhiwant,... - 《Optics...
It is proved, in particular, that every normal matrix with respect to an indefinite inner product defined by an invertible Hermitian matrix having at most two negative (or at most two positive) eigenvalues, admits a polar decomposition. Previously known descriptions of indecomposable normals in ...
This paper addresses the estimation of the center frequency of complex exponential signals with time-varying amplitude. A method which requires few assumptions regarding the signal’s envelope is proposed. It is based on the polar decomposition of a certain covariance matrix. The polar decomposition,...
Within the framework of hyperelastic materials, the polar decomposition theorem of Trusdell and Noll * occupies a position of primary importance. The polar decomposition theorem states that any deformation gradient tensor can be multiplicatively decomposed into the product of an orthogonal tensor, known...
This paper addresses the estimation of the center frequency of complex exponential signals with time-varying amplitude. A method, which requires few assumptions regarding the signal's envelope is proposed. It is based on the polar decomposition of a certain covariance matrix. The polar decomposition,...
The trajectory matrix H is an L × 2 K matrix and is transformed into the sum of biorthogonal matrices of rank 1, S=HHT, that is decomposed by singular value decomposition (Golyandina and Stepanov 2005). The singular value decomposition of trajectory matrix H is expressed as follows: ...
R. Johnson,“Matrix Analysis”,剑桥大学出版社,1985 年。 [2] N. J. Higham,“矩阵函数:理论与计算”,SIAM,2008 年。例子:>>> import numpy as np >>> from scipy.linalg import polar >>> a = np.array([[1, -1], [2, 4]]) >>> u, p = polar(a) >>> u array([[ 0.85749293, ...