Linjeralgebra

Linjeralgebra is the branch of mathematics that studies vector spaces, linear mappings between them, and systems of linear equations. It deals with vectors, which are geometric objects that have both magnitude and direction, and with matrices, which are rectangular arrays of numbers.

Key concepts in linjeralgebra include vectors, matrices, determinants, eigenvalues, eigenvectors, and vector spaces. Vectors can be added and scaled, and these operations form the basis of linear combinations. Matrices can be added, subtracted, multiplied, and inverted, and they represent linear transformations from one vector space to another. Determinants are scalar values associated with square matrices that provide information about the matrix's invertibility and the scaling factor of the transformation it represents. Eigenvalues and eigenvectors are special pairs associated with a linear transformation that reveal fundamental properties of the transformation, such as its directions of stretching or compression. A vector space is a collection of vectors that is closed under vector addition and scalar multiplication.

Linjeralgebra has widespread applications in various fields, including physics, engineering, computer graphics, economics, and statistics. For instance, it is used in solving systems of linear equations that arise in circuit analysis, in representing and manipulating 3D objects in computer graphics, and in statistical methods like regression analysis. The study of linjeralgebra provides a powerful framework for understanding and solving problems involving linear relationships.