Informatization or informatisation refers to the extent by which a geographical area, an economy or a society is becoming information-based, i.e. the increase in size of its information labor force. Usage of the term was inspired by Marc Porat’s categories of ages of human civilization: the Agricultural Age, the Industrial Age and the Information Age. Informatization is to the Information Age, it has been stated that: The Agricultural Age has brought about the agriculturization of the planet. The Industrial Age has caused among other things the industrialization of agriculture; the Information Age has resulted to the informatization of the agricultural industry. The term has been used within the context of national development. Everett Rogers defines informatization as the process through which new communication technologies are used as a means for furthering development as a nation becomes more and more an information society. However, some observers, such as Alexander Flor have cautioned about the negative impact of informatization on traditional societies.

The technological determinism dimension has been highlighted in informatization. Randy Kluver of Texas A&M University defines informatization as the process by which information technologies, such as the World Wide Web and other communication technologies, have transformed economic and social relations to such an extent that cultural and economic barriers are minimized. Kluver expands the concept to encompass the cultural arenas, he believes that it is a process whereby information and communication technologies shape cultural and civic discourse. G. Wang describes the same phenomenon which she calls "informatization" as a "process" of change that features the use of informatization and IT to such an extent that they become the dominant forces in commanding economic, political and cultural development; the term informatisation was coined by Simon Nora and Alain Minc in their publication L'Informatisation de la société: Rapport à M. le Président de la République, translated in English in 1980 as The Computerization of Society: A report to the President of France.

However, in an article published in 1987 Minc preferred to use informatisation and not computerization. After the 1978 publication the concept was adopted in French and English subject literatures and was broadened to include more aspects than only computers and telecommunications. Informatization has many far-reaching consequences in society. Kim observes that these include repercussions in economics and other aspects of modern living. In the economic sphere, for example, information is viewed as a focal resource for development, replacing the centrality of labor and capital during the industrial age. In the political arena, there are increased opportunities for participative democracy with the advent of information and communication technology that provide easy access to information on varied social and political issues. Industrialization propelled transformation of the economic system from agricultural age to modernized economies, so informatization ushered the industrial age into an information-rich economy.

Unlike the agricultural and industrial ages where economics refers to optimization of scarce resources, the information age deals with maximization of abundant resources. Alexander Flor wrote that informatization gives rise to information-based economies and societies wherein information becomes a dominant commodity or resource; the accumulation and efficient use of knowledge has played a central role in the transformation of the economy. Over the years and informatization have "redefined industries, politics and the underlying rules of social order". Although they explain different phenomena, their social, political and cultural functions remarkably overlaps. "Although globalization refers to the integration of economic institutions, much of this integration occurs through the channels of technology. Although international trade is not a new phenomenon, the advent of communications technologies has accelerated the pace and scope of trade". A) Globalization and Informatization will have great impact on cultural and social consequences of society.b) "Globalization and informatization are to diminish the concept of the national as a political institution".

Friedman argues that as nation states decline in importance, multi-national corporations, nongovernmental organizations, "superempowered individuals" such as George Soros gain influence and importance. As these non-political organizations and institutions gain importance, there are inevitable challenges to political and cultural processes.c) On the other hand and informatization allow for efficient flow of information. Individuals and societies are, therefore empowered to engage in international arena for economic and cultural resources.d) "There is proliferation of information about lifestyles and cultural issues. The telecommunications and computer networks allow for unprecedented global activism; this democratization of information increases the potential for international harmony, although it by no means guarantees it".e) These twin forces affects "centuries of tradition, local autonomy, cultural integrity."f) "Finally, one of the most devastating impact of the forces of globalization and informatization is that there is created an insidious conflic

Min-max theorem

In linear algebra and functional analysis, the min-max theorem, or variational theorem, or Courant–Fischer–Weyl min-max principle, is a result that gives a variational characterization of eigenvalues of compact Hermitian operators on Hilbert spaces. It can be viewed as the starting point of many results of similar nature; this article first discusses the finite-dimensional case and its applications before considering compact operators on infinite-dimensional Hilbert spaces. We will see that for compact operators, the proof of the main theorem uses the same idea from the finite-dimensional argument. In the case that the operator is non-Hermitian, the theorem provides an equivalent characterization of the associated singular values; the min-max theorem can be extended to self-adjoint operators. Let A be a n × n Hermitian matrix; as with many other variational results on eigenvalues, one considers the Rayleigh–Ritz quotient RA: Cn \ → R defined by R A = where denotes the Euclidean inner product on Cn.

The Rayleigh quotient of an eigenvector is its associated eigenvalue. Equivalently, the Rayleigh–Ritz quotient can be replaced by f =, ‖ x ‖ = 1. For Hermitian matrices, the range of the continuous function RA, or f, is a compact subset of the real line; the maximum b and the minimum a are the smallest eigenvalue of A, respectively. The min-max theorem is a refinement of this fact. Let A be an n × n Hermitian matrix with eigenvalues λ1 ≤... ≤ λk ≤... ≤ λn λ k = min U and λ k = max U in particular, λ 1 ≤ R A ≤ λ n ∀ x ∈ C n ∖ and these bounds are attained when x is an eigenvector of the appropriate eigenvalues. The simpler formulation for the maximal eigenvalue λn is given by: λ n = max; the minimal eigenvalue λ1 is given by: λ 1 = min. Since the matrix A is Hermitian it is diagonalizable and we can choose an orthonormal basis of eigenvectors that is, ui is an eigenvector for the eigenvalue λi and such that = 1 and = 0 for all i ≠ j. If U is a subspace of dimension k its intersection with the subspace span isn't zero and hence there exists a vector v ≠ 0 in this intersection that we can write as v = ∑ i = k n α i u i and whose Rayleigh quotient is R A = ∑ i = k n λ i α i 2 ∑ i = k n α i 2 ≥ λ k and hence max ≥ λ k Since this is true for all U, we can conclude that min { max ∣ dim ⁡