Definition:Linear Algebra (Mathematical Branch)

This page is about Linear Algebra (Mathematical Branch). For other uses, see Linear Algebra.

Definition

Linear algebra is the branch of algebra which studies vector spaces and linear transformations between them.

Also see

• Results about linear algebra can be found here.

Linguistic Note

The word algebra originates from the Arabic word al-ğabr, meaning balancing, reduction or restoration.

It originates from the name of a book, circa $825$ C.E., by Muhammad ibn Musa al-Khwarizmi:

Al-Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala (The Compendious Book on Calculation by Completion and Balancing)

Sources

• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $3$: Field Theory: Vector Spaces, Bases, and Dimensions: $\S 90$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): linear algebra: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): linear algebra: 1.