Where does matrix collide?

A rectangular array of numbers, set out in rows and columns, together with the operations of addition and multiplication defined on such arrays. Arthur Cayley set out the idea in his 1858 A Memoir on the Theory of Matrices, treating the array as a single object that can be added, multiplied, and inverted, with a multiplication that does not commute. The referent is a formal object in algebra and its unit is an array of scalars, so what a matrix says is fixed entirely by its entries and the rules for combining them. It shares nothing with the other meanings but the word: no cells, no reporting lines, no rock, only numbers and the algebra that governs them.[1]

Unit

A rectangular array of numbers

Recovery means

Not applicable

Measured by

Defined by its entries and the operations of matrix algebra, not measured empirically

The network of proteins and polysaccharides that cells secrete and sit within, giving a tissue its structure and passing signals to the cells it surrounds. Richard Hynes, in his 2009 review The Extracellular Matrix: Not Just Pretty Fibrils, describes it as far more than inert scaffolding, a dynamic assembly of collagens, proteoglycans, and glycoproteins that guides how cells grow, move, and differentiate. The referent is a biological material outside the cell and its unit is the molecular mesh of a tissue. It is a matrix in that it is an enclosing medium, but the thing enclosed is living cells, and nothing here is numeric or organizational.[2]

Unit

The molecular network surrounding cells in a tissue

Recovery means

Not applicable

Measured by

Assayed biochemically and imaged as fibrillar networks in tissue

A structure in which staff report along two lines at once, typically to a functional manager and to a product or project manager, so that authority is shared rather than held in a single chain. Jay Galbraith set out the design in his 1971 paper Matrix Organization Designs, and Stanley Davis and Paul Lawrence developed it in their 1977 book Matrix, presenting it as a way to balance two demands the older single-line hierarchy could not meet together. The referent is a firm's reporting structure and its unit is the grid of dual authority. The word matrix here names a crossing of two axes of command, not an array of numbers and not a tissue.[3][4]

Unit

A dual-authority reporting structure

Recovery means

Not applicable

Measured by

Described by the reporting lines drawn on an organization chart