Линейная алгебра. Шпаргалка

Basic formulas for the course Linear Algebra. Theory, properties, formulas

Linear algebra is a branch of mathematics within the framework of which the most diverse objects of linear nature are studied. Among such objects include linear equations and spaces, maps, etc.

Elements of linear space are called vectors, generalizing a term from vector algebra. Linear space itself is often called vector space.

Linear spaces are one of the most common mathematical objects, and the use of linear algebra is far from exhaustive in vector and matrix algebras.

Content:

- Matrices. Terminology and Notation

- Actions with matrices

- Summation procedures. Transposing

- Elementary matrix transformations

- Keys

- Qualifier properties

- Inverse matrix

- The concepts of bound and free vectors.

- Linear operations on rams

- Coordinates and components

- Projection of v-ra on an axis

- Division of the segment in this regard

- The normal equation of a line. General equation of the line

- The equation of a line on a plane passing through a given point perpendicular to a given direction

- Study of the equation of the line incomplete ur straight line

- Equation of a line with an angular coefficient

- Ur straight, passage through a given t., With a given angular coefficient. Ur direct passage through two given points

- The distance from a point to a line on a plane

- The equation of a line in segments

- The canonical equation of the line

- Parametric equation of a line on a plane

- The angle between two lines on the plane

- The normal equation of the plane. The general equation of the plane.

- ur plane passing through a given point perpendicular to a given direction

- The equation of a plane passing through three given points

- distance from point to plane

- The angle between two planes, the conditions of parallelism and perpendicularity of two planes

- Parametric equations of a straight line in space

- The canonical equation of a straight line in space

- The equation of a line in space passing through two given points

- The general equation of a straight line in space. transition to canonical equations

- The angle between the lines in space. The conditions of parallelism and perpendicularity of two lines

- The angle between the line and the plane. The conditions of parallelism and perpendicularity of a straight line and a plane