Where does determinant collide?

In linear algebra a determinant is a single number computed from the entries of a square array of numbers (a matrix) that records whether the array can be inverted and how it scales areas or volumes. Augustin-Louis Cauchy's 1815 memoir gave the word déterminant its modern meaning as this scalar, building on the earlier equation-solving rules of Leibniz (1693) and Cramer (1750), and the idea was later folded into the theory of matrices. A determinant of zero means the array collapses its inputs and cannot be reversed. The referent here is a computed quantity attached to a table of numbers, and it has nothing in common with a chemical patch on an antigen or a social condition that shapes health.[1]

Unit

A single scalar value computed from an n by n square matrix

Recovery means

Not applicable

Measured by

Computed by cofactor expansion, by row reduction, or as the product of a matrix's eigenvalues

In immunology a determinant, or antigenic determinant, is the specific small region of a molecule that an antibody or immune receptor actually binds and recognizes. Karl Landsteiner's studies of serological specificity, collected in The Specificity of Serological Reactions (1936), showed that a small, chemically defined group on a large molecule governs which antibodies will bind it, and the recognized region is also called the epitope (Jerne, 1960). A single protein can carry many such determinants, each a distinct binding target. The referent is a physical patch on a molecule that triggers recognition, unlike a number computed from a matrix or a social condition that influences a population's health.[2][3]

Unit

One binding region on an antigen, recognized by one antibody or receptor

Recovery means

Not applicable

Measured by

Mapped by binding assays, competition experiments, and structural methods such as X-ray crystallography

In public health a determinant, in the phrase social determinants of health, is a condition of the social and economic environment (such as income, housing, education, or working conditions) that shapes how healthy people are and how long they live. The named construct was set out in Marmot and Wilkinson's edited volume Social Determinants of Health (1999) and stated for a wide audience in Marmot's 2005 Lancet paper Social determinants of health inequalities, which argued that the social conditions in which people live largely account for gaps in health between groups. These determinants are studied at the level of populations rather than individual biology. The referent is a social or economic cause of health outcomes, and it is unrelated to a scalar drawn from a matrix or a binding region on an antigen.[4][5]

Unit

A social or economic condition acting across a population

Recovery means

Not applicable

Measured by

Assessed by linking social and economic indicators to health outcomes across populations