Also known as matrix rank, rank of matrix, rank of a matrix
measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by a matrix
In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns. This corresponds to the maximal number of linearly independent columns of A. This, in turn, is identical to the dimension of the vector space spanned by its rows. Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.
The rank is commonly denoted by rank(A) or rk(A); sometimes the parentheses are not written, as in rank A. The rank can also be denoted by rg(A), from German Rang.
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Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).