Kolmogorov's complexity for positive definite matrices (Q5957191)

Using the complexity for graphs introduced by Kolmogorov, the authors define the complexity of positive definite matrices with respect to a unit vector. They show that the complexity range coincides with the logarithm of the matrix spectrum, the induced order equals to the spectral order, and that this order is stronger than that one induced by the operator entropy. Finally they observe that almost all the obtained results hold for positive operators on a Hilbert space.