How to interpret the norm of a matrix?

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What's geometric interpretation of the Euclidean (Frobenius) norm of the matrix?

I know that vector norm is a vector's lenght but what is the matrix norm geometrically?

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Answer was given by Anton Zagrivin.

Consider the matrix as the operator on your vector space. Imagine the unit ball in this space; apply your operator to that unit ball; the lenght of the longest vector in the image of the unit ball will be the norm of the operator