The $2$-norm of a tubal matrix is equal to its largest T-singular value, multiplied with a coefficient, which is $1$ in the case of matrices . Further study on tubal matrices may reveal more links between matrix theory and tensor theory . We define positive semi-definite symmetrictubal scalars such that they are still corresponding to third order s-diagonal tensors, which were recently used for studying the T-SVD factorizations . We show that T-Singular values of tubalmatrix matrices are natural extensions of singular valuesof matrices. This shows that the$2$ norm of a . tubal . matrices is . equal to the . largest . value, multiplying with a . coefficient, multipliedwith a coefficient which is . $1$. in the . case of the .

Author(s) : Liqun Qi

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Keywords : matrices - tubal - matrix - singular - coefficient -

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