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In term of the mathematical distance measurement, What is the significance of a Frobenius norm for a binary matrix?

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The Frobenius norm of a binary matrix is the square root of the number of non-zero elements.

Let the point (0.,...0) be the origin, and let's say the vec'd binary matrix elements are the coordinates of a point, with coordinates being zero or one. Then the Frobenius norm is the Euclidean distance from the origin to that point.

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