15 Facts About Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as:.

For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations.

Linear algebra is used in most sciences and fields of engineering, because it allows modeling many natural phenomena, and computing efficiently with such models.

Linear algebra realized the connection between matrices and determinants, and wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".

Linear algebra is flat differential geometry and serves in tangent spaces to manifolds.

Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra.

The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.

Until the 19th century, linear algebra was introduced through systems of linear equations and matrices.

Linear algebra is concerned with those properties of such objects that are common to all vector spaces.

Linear algebra maps are mappings between vector spaces that preserve the vector-space structure.

An essential question in linear algebra is testing whether a linear map is an isomorphism or not, and, if it is not an isomorphism, finding its range and the set of elements that are mapped to the zero vector, called the kernel of the map.

Linear algebra endomorphism is a linear map that maps a vector space to itself.

Linear algebra form is a linear map from a vector space over a field to the field of scalars, viewed as a vector space over itself.

Linear algebra is used in almost all areas of mathematics, thus making it relevant in almost all scientific domains that use mathematics.

Linear algebra is thus a fundamental part of functional analysis and its applications, which include, in particular, quantum mechanics .