There seems to be widespread confusion about the use of the words
*minimum* and *minima* (along with *maximum / maxima*)
in a mathematical context.

These and a number of other words, all borrowed from Latin or Greek, have potentially confusing singular and plural forms.

In fact, *minimum* is the singular form, just as in normal
English usage, and *minima* refers to two or more. Thus we can
talk about *x* = *a* being *a local minimum* of a function
*f*(*x*), meaning that for *x* = *a*,
*f*(*x*) has a value that is lower than for nearby values
of *x*.

A function will often have several local *minima*, however - that is,
several dips in its graph. (A local *minimum* is actually the *bottom*
of a dip.)

One of these dips/minima will be lower than all the rest. In the
scenario in the diagram, this lowest local minimum is referred to as
the *global minimum*. Note that *global* means "everywhere";
there can only be one global minimum for *f*(*x*).
In particular, it doesn't make sense to talk about ??"a global minima"
(because "a" implies singular, and "minima" implies plural)
or to talk about "global minima" unless you are talking about minima
of two or more different functions.

"Local minima" of a function makes sense (assuming the function has more than one local minimum), but ??"a local minima" and ??"a minima" still are not right, as once again, "a" implies singular, and "minima" implies plural.

Similar rules apply to
*maximum* and *maxima*,
*extremum* and *extrema*, and
*optimum* and the less often used *optima*.

Singular | Singular example | Plural | Plural example |
---|---|---|---|

criterion | satisfy a criterion | criteria | several criteria |

automaton | this automaton | automata | several deterministic automata |

matrix | this matrix has eigenvalues ... | matrices | these symmetric matrices ... |

vertex | find a vertex ... | vertices | a triangle has 3 vertices |

datum | this single datum | data | this collection of data |

schema | here is a schema for for-loops | schemata | some schemata for for-loops and if-statements |

Plural | Singular |
---|---|

abscissae | abscissa |

addenda | addendum |

algae | alga |

alumnae | alumna |

alumni | alumnus |

alveoli | alveolus |

analyses | analysis |

annuli | annulus |

antennae | antenna |

appendices | appendix |

aquaria | aquarium |

atria | atrium |

automata | automaton |

axes | axis |

bacilli | bacillus |

bronchi | bronchus |

cacti | cactus |

caesurae | caesura |

calculi | calculus |

catharses | catharsis |

cicatrices | cicatrix |

colloquia | colloquium |

colossi | colossus |

compendia | compendium |

consortia | consortium |

continua | continuum |

corpora | corpus |

corrigenda | corrigendum |

crania | cranium |

crises | crisis |

criteria | criterion |

curricula | curriculum |

data | datum |

desiderata | desideratum |

diaereses | diaeresis |

diagnoses | diagnosis |

dicta | dictum |

directrices | directrix |

dodecahedra | dodecahedron |

effluvia | effluvium |

ellipses | ellipsis |

emphases | emphasis |

encomia | encomium |

ephemerides | ephemeris |

equilibria | equilibrium |

errata | erratum |

esophagi | esophagus |

extrema | extremum |

foci | focus |

fungi | fungus |

genera | genus |

genii | genius |

honoraria | honorarium |

icosahedra | icosahedron |

incubi | incubus |

infima | infimum |

lacunae | lacuna |

loci | locus |

magi | magus |

matrices | matrix |

maxima | maximum |

media | medium |

memoranda | memorandum |

millenia | millenium |

minima | minimum |

minutiae | minutia |

moduli | modulus |

mycobacteria | mycobacterium |

nebulae | nebula |

neuroses | neurosis |

nuclei | nucleus |

nucleoli | nucleolus |

octahedra | octahedron |

opera | opus |

optima | optimum |

ova | ovum |

periphrases | periphrasis |

phenomena | phenomenon |

phyla | phylum |

placentae | placenta |

pleurae | pleura |

podia | podium |

polyhedra | polyhedron |

psychoses | psychosis |

pudenda | pudendum |

pupae | pupa |

quanta | quantum |

radices | radix |

radii | radius |

referenda | referendum |

rhombi | rhombus |

rostra | rostrum |

sacra | sacrum |

sanataria | sanatarium |

sanatoria | sanatorium |

sarcophagi | sarcophagus |

scapulae | scapula |

schemata | schema |

septa | septum |

sera | serum |

simplices | simplex |

simulacra | simulacrum |

solaria | solarium |

spectra | spectrum |

spermatozoa | spermatozoon |

stadia | stadium |

sterna | sternum |

stigmata | stigma |

stimuli | stimulus |

strata | stratum |

substrata | substratum |

succubi | succubus |

syllabi | syllabus |

symposia | symposium |

synopses | synopsis |

syntheses | synthesis |

termini | terminus |

testes | testis |

tetrahedra | tetrahedron |

theses | thesis |

thromboses | thrombosis |

tori | torus |

tumuli | tumulus |

ultimata | ultimatum |

umbilici | umbilicus |

verrucae | verruca |

vertebrae | vertebra |

vertices | vertex |

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