scalar

/'skeilə/

Thân thiện

A scientist writes the scalar quantity "5 kg" on a whiteboard.

Definition

1. Adjective:

   • Relating to a magnitude without direction: Describes a quantity that is fully defined by its magnitude alone, not requiring any directional information. Examples include mass, temperature, and speed.
   • Relating to a musical scale: Pertaining to or consisting of the notes of a scale.

2. Noun:

   • A scalar quantity: A variable or physical quantity that is described solely by a magnitude (a single numerical value) and has no direction.

Usage Examples

• Adjective:

  • Mass and temperature are scalar quantities, unlike force which is a vector.
  • The guitarist practiced scalar exercises to improve his finger dexterity.

• Noun:

  • In this equation, the symbol 'm' represents a scalar.
  • Speed is a scalar, whereas velocity is a vector.

Advanced Usage

• Scalar field: In physics and mathematics, a region of space where a scalar quantity (like temperature or pressure) is assigned to every point.

  • The temperature map shows a scalar field across the country.

• Scalar multiplication: In linear algebra, the operation of multiplying a vector by a scalar (a single number), which scales the vector's magnitude.

  • The process of scalar multiplication changes the length of a vector but not its direction.

Variants and Related Words

• Scalarity (n, rare): The quality or state of being scalar.
• Scalariform (adj): Having a ladder-like pattern; this is a biological/technical term and is not directly synonymous but shares the Latin root (ladder, scale).

Synonyms

• Magnitude-only (descriptive phrase, for the mathematical sense).
• Non-directional (descriptive phrase).
• Scale-based (for the musical sense).

Antonyms

• Vectorial (adj): Relating to or having the properties of a vector (a quantity with both magnitude and direction).
• Vector (n): A quantity having direction as well as magnitude.

Học thuật

Adjective

1. of or relating to a directionless magnitude (such as mass or speed etc.) that is completely specified by its magnitude
   • scalar quantity
2. of or relating to a musical scale
   • he played some basic scalar patterns on his guitar

Noun

1. a variable quantity that cannot be resolved into components