rank-deficient.

Having a matrix rank lower than the smaller of its numbers of rows and columns.

Use it for

Words that belong together

• rank-deficient matrix
• rank-deficient design
• rank-deficient least-squares problem

On the page

The duplicated columns made the design matrix rank-deficient.

The solver used a minimum-norm solution for the rank-deficient least-squares problem.

Usage notes

Primary category: academic / formal / analytical. Lexical Type: Word. Forms: Normally non-gradable; no ordinary comparative or superlative. Commonness: uncommon (editorial estimate; not a corpus frequency statistic). Legacy lexical fields mirror sense 1; numbered fields keep each relevant meaning separate. Research distinction: UCLA linear-algebra lecture directly read: full rank equals minimum of row and column dimensions; deficient least squares has nonunique solutions and a minimum-norm solution. Positive indexed DTU/SIAM book description directly read explicitly uses rank-deficient and distinguishes exact or near numerical deficiency. No unseen book chapters claimed. Individually useful in research, criticism, methodology or conceptual analysis. Definitions and examples are original; no mood or intensity assigned to neutral analytical concepts. Commonness is an editorial estimate, not a frequency statistic. Writing functions: redundant analytical dimensions, nonunique coefficient estimates.