Chapter II.7

Applications

[12/67%]

Section II.7.1The norm and functions of a linear operator[10/70%]

Subsection II.7.1.1Norm of a linear operator

Subsection II.7.1.2Functions of linear operators

Subsection II.7.1.3Exponential

Subsection II.7.1.4One-parameter subgroups of the linear group

Subsection II.7.1.5Spectral radius

Section II.7.2Linear differential equations

Subsection II.7.2.1The derivative of the exponential function

Subsection II.7.2.2Differential equations

Subsection II.7.2.3A linear differential equation of order

n

Section II.7.3Convex polyhedra and linear programming[2/50%]

Subsection II.7.3.1Problem statement

Subsection II.7.3.2Motivation

Subsection II.7.3.3Main geometric concepts

Section II.7.4Non-negative matrices

Subsection II.7.4.1Production motivation

Subsection II.7.4.2Properties of non-negative matrices

Subsection II.7.4.3Stochastic matrices

Section II.7.5Lobachevsky geometry

Subsection II.7.5.1Hyperbolic space

Subsection II.7.5.2Isometries of the Lobachevsky space

Subsection II.7.5.3Lobachevsky metric

Subsection II.7.5.4The Lobachevsky plane

Section II.7.6Unsolved problems

Subsection II.7.6.1Strassen's Problem

Subsection II.7.6.2Orthogonal decompositions

Subsection II.7.6.3Finite projective planes

Subsection II.7.6.4Bases of spaces and Latin squares