How to write this sentence about the square root of a matrix [closed]

Suppose in a math paper I formulated the following sentence:

The square root of the matrix A is well-defined, denoted by √A

A friend of mine told me that it sounds not correct.

closed as unclear what you're asking by Chenmunka, Mr. Shiny and New 安宇, choster, phenry, Ellie KesselmanNov 8 '14 at 7:31

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• Whether it's correct depends on the rest of the sentence. Can you include it? – Peter Shor Nov 3 '14 at 1:04

The words defined and denoted right after each other may cause a bit of confusion which can be resolved like this:

The square root of the matrix A, denoted by √A, is well-defined.

There is nothing wrong with your sentence. You use the appropriate punctuation (`,`) to give a break in the sentence letting the reader see that

denoted by √A

is the next part of the sentence and the word denoted belongs to √A joined by the word by

the sentence up to the comma is a complete thought and can stand on its own.

The square root of the matrix A is well-defined.

• “The square root of the matrix A is defined by √A” is a false statement, so will not remove confusion. The root can be denoted by √A, but must be defined by some relation like (√A)² = A. (See ref) Also note, well-defined is a mathematical idiom, and its meaning is not deducible from meanings of well and defined. – James Waldby - jwpat7 Nov 9 '14 at 0:44