Linear algebra is the cornerstone of analytic geometry. /kloc-In the 7th century, Descartes and Fermat introduced the coordinate system into the geometric space, thus establishing a bridge between geometry and algebra. Through analytic geometry, linear algebra can be expressed concretely.

For example, in analytic geometry, we can use the coordinate representation of vectors to describe vectors, use matrices to represent linear transformations, and use determinants to solve cross products. This knowledge of linear algebra provides a powerful tool for analytic geometry.

Secondly, linear algebra is the generalization and abstraction of analytic geometry. Analytic geometry mainly studies geometric problems in Euclidean space, while linear algebra extends the concepts and conclusions in analytic geometry to general vector space. For example, the concepts of vector space, linear transformation, eigenvalues and eigenvectors in linear algebra can all be regarded as the generalization of the corresponding concepts in analytic geometry.

Thirdly, linear algebra and analytic geometry promote each other in research methods. Analytic geometry transforms geometric problems into algebraic problems by introducing coordinate systems, so that geometry can be studied by algebraic methods. Linear algebra provides a deeper theoretical basis for analytic geometry by studying mathematical objects such as vectors, matrices and determinants.

For example, in analytic geometry, we can use linear equations to solve the intersection of straight lines, use determinant to calculate the cross product, and use matrix to represent linear transformation. The knowledge of linear algebra provides a richer means for the study of analytic geometry.

Finally, linear algebra and analytic geometry complement each other in practical applications. Linear algebra is widely used in physics, computer science, economics and other fields, while analytic geometry has important application value in engineering, geometry, topology and other fields. Linear algebra and analytic geometry complement each other, which makes it widely used in various fields.

Linear algebra is widely used in physics, computer science, economics and other fields, while analytic geometry has important application value in engineering, geometry, topology and other fields.