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Totally Nonnegative Matrices by Charles R. Johnson, Shaun M. Fallat

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Chapter Five

The Spectral Structure of TN Matrices

5.0 INTRODUCTION

By “spectral structure” we mean facts about the eigenvalues and eigenvectors of matrices in a particular class. In view of the well-known Perron-Frobenius theory that describes the spectral structure of general entrywise nonnegative matrices, it is not surprising that TN matrices have an important and interesting special spectral structure. Nonetheless, that spectral structure is remarkably strong, identifying TN matrices as a very special class among nonnegative matrices. All eigenvalues are nonnegative real numbers, and the sign patterns of the entries of the eigenvectors are ...

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