Definition:Magnitude

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Definition

The magnitude (or size) of a quantity (either vector or scalar) is a measure of how big it is.

It is usually encountered explicitly in the context of vectors:

If $\mathbf v$ is the vector quantity in question, then its magnitude is denoted:

$\size {\mathbf v}$

or

$v$

Also defined as

In Euclidean number theory, the term magnitude is used to mean positive real number.

Also known as

The magnitude of a vector is also referred to as its module or modulus in some older books.

Some sources refer to it as the absolute value of the vector.

Also see

• Definition:Direction

• Definition:Vector Length
• Definition:Absolute Value

Sources

• 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Definitions: $3$. Definitions of terms
• 1927: C.E. Weatherburn: Differential Geometry of Three Dimensions: Volume $\text { I }$ ... (previous) ... (next): Introduction: Vector Notation and Formulae
• 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: $1$. Scalar and Vector Quantities
• 1966: Isaac Asimov: Understanding Physics ... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $3$: The Laws of Motion: Forces and Vectors
• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 22$: Vectors and Scalars
• 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.2$ Rotation of Coordinates
• 1975: Patrick J. Murphy: Applied Mathematics Made Simple (revised ed.) ... (previous) ... (next): Chapter $1$: Mechanics: $(2)$ Characteristics of a Force: $\text{(c)}$

in which context it is applied to a force only

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $-1$ and $i$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $-1$ and $i$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): absolute value: 3.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): absolute value: 3.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): magnitude (of a vector)