Basis vs. Dimension

A physical base or foundation.

A starting point, base or foundation for an argument or hypothesis.

An underlying condition or circumstance.

A regular frequency.

Example: ‘You should brush your teeth on a daily basis at minimum.’; ‘The flights to Fiji leave on a weekly basis.’; ‘Cars must be checked on a yearly basis.’;

(linear algebra) In a vector space, a linearly independent set of vectors spanning the whole vector space.

(accounting) Amount paid for an investment, including commissions and other expenses.

(topology) A collection of subsets ("basis elements") of a set, such that this collection covers the set, and for any two basis elements which both contain an element of the set, there is a third basis element contained in the intersection of the first two, which also contains that element.

Example: ‘The collection of all possible unions of basis elements of a basis is said to be the topology generated by that basis.’;

The foundation of anything; that on which a thing rests.

The pedestal of a column, pillar, or statue.

Example: ‘If no basis bear my rising name.’;

The groundwork; the first or fundamental principle; that which supports.

Example: ‘The basis of public credit is good faith.’;

The principal component part of a thing.

a relation that provides the foundation for something;

Example: ‘they were on a friendly footing’; ‘he worked on an interim basis’;

the fundamental assumptions from which something is begun or developed or calculated or explained;

Example: ‘the whole argument rested on a basis of conjecture’;

the most important or necessary part of something;

Example: ‘the basis of this drink is orange juice’;

A single aspect of a given thing.

A measure of spatial extent in a particular direction, such as height, width or breadth, or depth.

A construct whereby objects or individuals can be distinguished.

(geometry) The number of independent coordinates needed to specify uniquely the location of a point in a space; also, any of such independent coordinates.

(linear algebra) The number of elements of any basis of a vector space.

(physics) One of the physical properties that are regarded as fundamental measures of a physical quantity, such as mass, length and time.

Example: ‘The dimension of velocity is length divided by time.’;

(computing) Any of the independent ranges of indices in a multidimensional array.

An alternative universe or plane of existence.

(transitive) To mark, cut or shape something to specified dimensions.

Measure in a single line, as length, breadth, height, thickness, or circumference; extension; measurement; - usually, in the plural, measure in length and breadth, or in length, breadth, and thickness; extent; size; as, the dimensions of a room, or of a ship; the dimensions of a farm, of a kingdom.

Example: ‘Gentlemen of more than ordinary dimensions.’;

Extent; reach; scope; importance; as, a project of large dimensions.

The degree of manifoldness of a quantity; as, time is quantity having one dimension; volume has three dimensions, relative to extension.

A literal factor, as numbered in characterizing a term. The term dimensions forms with the cardinal numbers a phrase equivalent to degree with the ordinal; thus, a2b2c is a term of five dimensions, or of the fifth degree.

The manifoldness with which the fundamental units of time, length, and mass are involved in determining the units of other physical quantities.

the magnitude of something in a particular direction (especially length or width or height)

a construct whereby objects or individuals can be distinguished;

Example: ‘self-confidence is not an endearing property’;

one of three cartesian coordinates that determine a position in space

magnitude or extent;

Example: ‘a building of vast proportions’;

indicate the dimensions on;

Example: ‘These techniques permit us to dimension the human heart’;

shape or form to required dimensions

a measurable extent of a particular kind, such as length, breadth, depth, or height

Example: ‘the drawing must be precise in dimension’; ‘the final dimensions of the pond were 14 ft x 8 ft’;

a mode of linear extension of which there are three in space and two on a flat surface, which corresponds to one of a set of coordinates specifying the position of a point.

an expression for a derived physical quantity in terms of fundamental quantities such as mass, length, or time, raised to the appropriate power (acceleration, for example, having the dimension of length × time⁻²).

an aspect or feature of a situation

Example: ‘we must focus on the cultural dimensions of the problem’;

cut or shape (something) to particular measurements.

mark (a diagram) with measurements.

In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line.