Definition:Linear Algebra (Mathematical Branch)

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: $\S 90$