"Elements are zero" vs "elements are zeros"

Either is grammatically justifiable but "the elements are zero" reads more naturally. In mathematics, there's only one zero so, when you write "the elements are zeroes", it feels like you're drawing attention to the multiple instances of the symbol "0", rather than the single concept they all refer to.

Zero is the correct form. The confusion seems to be a misunderstanding between two languages: English and Mathematics.

matrix

a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

The "elements" are the intersections of each row and each column, with each element containing a mathematical value: a number, a symbol, or an expression.

The individual items in a matrix are called its elements or entries.

There is precisely one value in each element of a matrix. (Even if that value is another matrix containing 10,000 elements, it is considered a single value.)

As mathematicians, we say this sentence:

"a sparse matrix is a matrix in which most of the elements are zero."

The understood meaning of the sentence is:

"a sparse matrix is a matrix in which most of the elements [equal] zero."

OR its equivalent:

"a sparse matrix is a matrix in which most of the elements [have a value of] zero."

OR its equivalent:

"a sparse matrix is a matrix in which most of the elements are empty."

The plural zeros is not consistent with the mathematical meaning of the statement, because it implies that the elements have "more than one value" which defies the mathematical definition of element with respect to a matrix.