{"id":"matrix","domain":"algebra","type":"Concept","title":"Matrix","slug":"matrix","url":"/mathematics/algebra/matrix/","summary":"A rectangular grid of numbers representing a linear transformation. Term coined by Sylvester (1850); systematic theory by Cayley (1850s-60s).","added_to_codex":"2026-05-27","last_verified":"2026-05-27","sources":[{"tier":1,"citation":"Strang, G. (2016). Introduction to Linear Algebra. 5th ed. Wellesley-Cambridge Press."},{"tier":1,"citation":"Horn, R.A. and Johnson, C.R. (2012). Matrix Analysis. 2nd ed. Cambridge University Press."},{"tier":2,"citation":"Strassen, V. (1969). Gaussian elimination is not optimal. Numerische Mathematik, 13(4), 354-356."},{"tier":3,"citation":"Kline, M. (1972). Mathematical Thought from Ancient to Modern Times. Oxford University Press."}],"relationships":[{"type":"represents","target":"vector-space","label":"Vector Space — linear transformations"},{"type":"key_computation","target":"determinant","label":"Determinant"},{"type":"forms","target":"ring","label":"Ring — square matrices"}],"entry_status":"live","reading_levels_available":["curious","exploring","deep_dive"],"completeness":1.0,"codex_version":"1.7"}