以2为底的矩阵对数 [英] Matrix Logarithm in Base 2

问题描述

Logm()取矩阵的对数，而log2()取矩阵的每个元素的对数以2为底.

Logm() takes the matrix logarithm, and log2() takes the logarithm base 2 of each element of a matrix.

我正在尝试计算冯·诺依曼熵，它涉及以2为底的矩阵对数.我该怎么做?

I'm trying to compute the Von Neumann entropy, which involves the base 2 matrix logarithm. How do I do this?

推荐答案

如果将矩阵指数以2为底"定义为B = expm(log(2) .* A)，或者类似地通过特征分解直接定义矩阵对数以2为底"在以特征值方式应用以2为底的标准对数的情况下，可以通过除以log(2)来获得对应的以2为底的矩阵对数:

If you define the matrix exponential "with base 2" as B = expm(log(2) .* A), or if you analogously directly define the matrix logarithm "with base 2" via an eigendecomposition with the standard logarithm of base 2 applied eigenvalue-wise, then you can obtain a corresponding base 2 matrix logarithm by dividing by log(2):

A = logm(B) ./ log(2)

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