Exploration and Analysis of a Method for Estimating the Rank of a Matrix

Matrix Rank;Rank Estimation;Hypothesis Testing

Orlowski, Nicholas Richard ; Dr. Donald Bitzer, Committee Member,Dr. Robert Funderlic, Committee Chair,Dr. David Thuente, Committee Member,Orlowski, Nicholas Richard ; Dr. Donald Bitzer ; Committee Member ; Dr. Robert Funderlic ; Committee Chair ; Dr. David Thuente ; Committee Member

University:North Carolina State University

关键词: Matrix Rank;    Rank Estimation;    Hypothesis Testing;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/505/etd.pdf?sequence=1&isAllowed=y

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【 摘 要 】

The singular value decomposition (SVD) provides important information about a matrix and its rank, including its singular values and singular vectors. Because of noise in a matrix and the limitations of binary representation, the calculated SVD of a matrix is necessarily an estimate of the true SVD of that matrix.Our method approximates the true singular values of a matrix by gathering samples of the calculated singular values of the matrix. With these approximations, we can use hypothesis testing to make quantitative statements about the magnitude of each singular value and the rank of the matrix.