Logarithmic Tensor Norm

The thesis concentrates on the logarithmic norm in numerical algebra. First, we review the definition and properties of the logarithmic matrix norm. Then, we define the logarithmic tensor norm. And prove its existence and properties. Particularly, we get the computational formulas of the logarithmic norm defined by tensor norm ||·||1,||·||∞ or tensor semi-norm|||A|||2.The computational formulas are easier to calculate and analysis than the definition formulas. For real tensor, we also get the the computational formulas defined by tensor norm||·||2. Finally, we define the logarithmic norm of tensor pencil and prove its properties.