Vector product (cross product)

Table of Contents

ELEMENTS OF LINEAR ALGEBRA (19p.) (LinAlgebra.pdf)

MATRICES

Operations on matrices

Rules of matrix arithmetic

Transpose of a matrix

Properties of the transpose

Elementary matrices

DETERMINANTS

Determinat of a matrix

Minors and cofactors

Properties of determinants

SYSTEMS OF LINEAR EQUATIONS

The elementary equation operations

Augmented matrix

Reduced row–echelon form of a matrix

Gaussian elimination and Gauss–Jordan elimination.

Fundamental theorem for system of linear equations.

Homogeneous linear systems

Matrix form of a linear system

Cramer’s rule

ALGEBRA OF VECTORS (16p.) (vectors.pdf)

COORDINATE SYSTEMS

The real line

Rectangular Cartesian coordinates of points in plane

Cartesian coordinates in space

SCALARS AND VECTORS

Vector arithmetic.

LINEAR COMBINATION OF VECTORS

Basis

Linear independence of vectors

Projection of vector on axis

VECTOR IN COMPONENT FORM

Vector in orthogonal Cartesian coordinate system

Direction cosines

The algebra of vectors

SCALAR PRODUCT (DOT PRODUCT)

Component form for the scalar product

The angle between vectors

VECTOR PRODUCT (CROSS PRODUCT)

Component form for the vector product

Evaluation of the cross product in terms of determinants

SCALAR TRIPLE PRODUCT

Vector triple product

CHANGE OF BASIS

Transformation of vector components

TRANSFORMATION OF COORDINATE SYSTEMS

Translation of axes

Rotation of axes

Rotation of axes in plane

Дата добавления: 2015-08-27