双正矩阵的一个等价条件

本文证明了实对称矩阵成为双正矩阵或严格双正矩阵的充分必要条件,此充分必要条件与所考虑实对称阵之主子矩阵的特征值及特征向量有关。

双正交小波矩阵

本文引进了双正交（半正交）小波矩阵及对偶的概念。讨论了这些矩阵的一些性质，尤其是给出了利用小波矩阵的元素将离散函数展开为级数形式的结果，进而建立了半正交小波矩阵与［８］中正交小波矩阵，双正交小波矩阵与对偶双正交小波矩阵的关系。最后举例说明了本文引进双正交（半正交）小波矩阵及对偶概念和方法的合理性。

基于双正交非负矩阵三因式的肿瘤识别

基因表达谱数据分析已经逐渐成为疾病诊断和分类的常规步骤.目前人们对NMF(nonnegative matrix factorization)的大多数研究都专注于二因式分解.论文另辟蹊径,对BONMTF(bi-orthogonal nonnegative matrix tri-factorization)算法进行了系统化的分析,利用此算法得到表征样本属性的矩阵,并将其应用于基因表达谱数据分析,提高了样本识别率.实验采用4组具有代表性的肿瘤基因表达谱数据,其结果证明了论文方法针对不同数据集的识别率都比传统方法有所提高,具有一定的可行性及应用前景.

A NOVEL APPROACH FOR DOA ESTIMATION IN UNKNOWN CORRELATED NOISE FIELDS

The key of the subspace-based Direction Of Arrival (DOA) estimation lies in the estimation of signal subspace with high quality. In the case of uncorrelated signals while the signals are temporally correlated, a novel approach for the estimation of DOA in unknown correlated noise fields is proposed in this paper. The approach is based on the biorthogonality between a matrix and its Moore-Penrose pseudo inverse, and made no assumption on the spatial covariance matrix of the noise. The approach exploits the structural information of a set of spatio-temporal correlation matrices, and it can give a robust and precise estimation of signal subspace, so a precise estimation of DOA is obtained. Its performances are confirmed by computer simulation results.

Matrix Approach in Wavelet Analysis

In this paper, we give a survey of matrix approach in wavelet theory , and describe some related results which were obtained by ourselves.