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The same grid of numbers in two delimiters, which are an array and a single number.
Brackets — square or round, the choice is house style — enclose a matrix: a rectangular array of entries. Straight vertical bars around the same grid denote its determinant, which is one number derived from the array. Swapping the delimiters therefore changes what has been written from a table into a scalar, and it is the commonest notational error in early linear algebra because the contents are identical and only the edges differ.
Brackets mark an array; straight bars mark the single number derived from it.
Drawn from the visual attributes recorded for each symbol. Only traits the two records disagree about are listed.
| Trait | Matrix brackets | Determinant bars |
|---|---|---|
| Built from | squares, lines and dots, number like | lines and dots, number like |
| Matrix brackets | Determinant bars | |
|---|---|---|
| What it denotes | An array of entries | A single number derived from a square array |
| Delimiter | Square or round brackets, interchangeably | Straight vertical bars, with no serif or curve |
| Shape it applies to | Any rectangle of entries | Square arrays only |
| What it tells you | The whole object | Whether the matrix is invertible, and how it scales area or volume |
| Relationship (from Symbolwise's records) | Commonly confused with Determinant bars — Brackets mark an array; straight bars mark the single number derived from it. | Commonly confused with Matrix brackets — Bars mark a derived number; brackets mark the array itself. |
ISO 80000-2:2019, Quantities and units — Part 2: Mathematics
International Organization for Standardization · retrieved 2026-07-31
Paywalled and NOT READ for this batch. Registered so the standard can be named as existing and as covering mathematical signs; it supports no meaning in any record. See docs/paywalled-standards.md.
AMS Style Guide — mathematical notation
American Mathematical Society · retrieved 2026-08-22
A publisher's house style rather than a standard. Authoritative about how notation is set in mathematical publishing; it does not decide what a symbol means.
Wikipedia · retrieved 2026-08-22
Tertiary reference, cited for the conventional description of a mark, its usual name and where it is encountered. Where an issuing body defines the mark, that body is cited alongside and governs.
Determinant bars are plain vertical strokes with nothing at either end. Floor and ceiling brackets are vertical strokes with a short foot or cap on one end only, and which end carries the serif says which way the number is rounded — feet at the bottom for the floor, caps at the top for the ceiling. At small type sizes and in handwriting the serif is the first thing lost, which is the whole of the confusion.
Alpha is a Greek letter and stands for a quantity — an angle, a coefficient, a significance level. The proportionality sign is an operator and stands between two quantities to say they keep a constant ratio. The drawings differ in that the proportionality sign's right-hand stroke runs out in an open curve rather than closing into the letter's tail.
Look at the left-hand edge. A straight flat back is an AND gate: the output is true only when every input is. A curved concave back is an OR gate: true when any input is. Everything else about the shapes is similar, which is why the back edge is worth checking deliberately rather than at a glance.
Look at what follows. A prefix never stands alone — it is glued to a unit symbol, as in kW or kg. A constant stands by itself in an equation. Careful physical writing subscripts the constant as k_B for exactly this reason, and the kelvin's capital K is a third claimant to the same letter.