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  Volume 6, Issue 4, Article 124
Lower Bounds for the Spectral Norm

    Authors: Jorma K. Merikoski, Ravinder Kumar,  
    Keywords: Spectral norm, Singular values.  
    Date Received: 20/12/04  
    Date Accepted: 01/09/05  
    Subject Codes:

15A60, 15A18.

    Editors: Simo Puntanen,  

Let $ mathbf{A}$ be a complex $ mtimes n$ matrix. We find simple and good lower bounds for its spectral norm $ Vert mathbf{A} Vert = max{  Vert mathbf{A}mathbf{x} Vert mid mathbf{x}inmathbb{C}^n,  Vert mathbf{x} Vert=1  }$ by choosing $ mathbf{x}$ smartly. Here $ VertcdotVert$ applied to a vector denotes the Euclidean norm.

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