vector algebra

Thân thiện

A student solves a problem on a chalkboard using vector algebra.

Definition

1. Noun:
   • The branch of mathematics: Specifically, the part of algebra concerned with the study of vectors, their operations (such as addition and scalar multiplication), and the structures formed by them, notably vector spaces.

Usage

• Vector algebra provides the foundational rules for manipulating quantities that have both magnitude and direction.
• It is a prerequisite for more advanced studies in linear algebra, physics, and engineering.

Examples

• Noun:
  • A solid understanding of vector algebra is essential for computer graphics programming.
  • The course covers the basics of vector algebra, including dot and cross products.

Advanced Usage

• "to apply vector algebra": To use the principles of vector algebra to solve a problem.
  • Engineers apply vector algebra to analyze forces in a structure.

Variants and Related Words

• Vector (n): A quantity having direction as well as magnitude.
• Vector space (n): A collection of vectors which may be added together and multiplied by scalars.
• Linear algebra (n): The broader branch of mathematics concerning vector spaces and linear mappings, which encompasses vector algebra.

Synonyms

• Algebra of vectors: A less common, descriptive synonym for vector algebra.

Related Phrases

• Laws of vector algebra: Refers to the commutative, associative, and distributive properties governing vector addition and scalar multiplication.

Học thuật

Noun

1. the part of algebra that deals with the theory of vectors and vector spaces