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Everything about Defective matrix
Non-diagonalizable matrix; one lacking a basis of eigenvectors
In linear algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an matrix is defective if and only if it does not have linearly independent eigenvectors. A complete basis is formed by augmenting the eigenvectors with generalized eigenvectors, which are necessary for solving defective systems of ordinary differential equations and other problems. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Defective matrixA 5-minute orientation
- Skim a recent paper: Defective extracellular matrix remodeling in brown adipose tissue is associated with fibro-inflammation and reduced diet-induced thermogenesisInfluential work since 2022
- Pick up a classic book: Тензорная тригонометрияThe most-reprinted book on the subject
- Read the landmark paper: Marfan syndrome: defective synthesis, secretion, and extracellular matrix formation of fibrillin by cultured dermal fibroblasts.Cited 202 times
- Go sideways: Triangular matrixA closely related topic
- Go sideways: Canonical basisA closely related topic
📖 Definitions
Noun A square (n×n) matrix that has fewer than n linearly independent eigenvectors, and is therefore not diagonalisable.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Marfan syndrome: defective synthesis, secretion, and extracellular matrix formation of fibrillin by cultured dermal fibroblasts.
Polycystic kidney disease: Primary extracellular matrix abnormality or defective cellular differentiation?
Overexpression of Lysyl Hydroxylase-2b Leads to Defective Collagen Fibrillogenesis and Matrix Mineralization
Defective translation of measles virus matrix protein in a subacute sclerosing panencephalitis cell line
Myh10 deficiency leads to defective extracellular matrix remodeling and pulmonary disease
Osteoblastic Response to the Defective Matrix in the Osteogenesis Imperfecta Murine (oim) Mouse
Extracellular matrix with defective collagen cross-linking affects the differentiation of bone cells
Altered distribution of bone matrix proteins and defective bone mineralization in klotho-deficient mice
🆕 Influential since 2022
Defective extracellular matrix remodeling in brown adipose tissue is associated with fibro-inflammation and reduced diet-induced thermogenesis
Synthesis of mixed matrix membrane utilizing robust defective MOF for size-selective adsorption of dyes
Thin selective layered mixed matrix membranes (MMMs) with defective UiO-66 induced interface engineering toward highly enhanced pervaporation performance
Vacancy-defective nano-carbon matrix enables highly efficient Fe single atom catalyst for aqueous and flexible Zn-Air batteries
Microstructure evolution and mechanical properties of graphene reinforced Ti-6Al-4V matrix composites: Defective vs high-quality graphene
📚 Books worth reading
Тензорная тригонометрияNinul Anatoly Sergeevich · 2004
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Modal matrix In linear algebra, the modal matrix is used in the diagonalization process involving eigenvalues and eigenvectors. Specifically the modal matrix M {\displaystyl…