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 ENGINEERING:LINEAR ALGEBRA FOR DATA ANALYSIS: PART2 Single value decomposition    A eigenvalue matrix can be decomposed into three matrices ,which represent two rotation of the vector and one scaling. A= P.V.Pinverse    A square ,symmetrical matrix can also be decomposed by a different method called single value decomposition. Suppose we have a circle with orthogonal radiii as vectors ,v1 and v2. If we stretch the circle into an ellipse these vectors change into new vectors , the major and minor axis.To allow this transformation of vectors the angle between them has to be orthogonal. Also the stretching can be incorporated by a scaling factor when the norm of the vector remains unchanged during the transformation. These properties occur in orthonormal matrices.      So the transformation of radii vectors can be represented by A. v= sigma. u. Here u matrix is called Principal Axis and sigma or scaling factor is called single value.    wh...

 ENGINEERING:LINEAR ALGEBRA FOR DATA ANALYSIS PART1 Vectors and Matrix   Vectors are mathematical objects with two or more components. In data analysis a vector can represent the person with components as height and weight.The components of a vector can be represented as two components in a Cartesian coordinate system ,one along x- axis the other along Y-axis; these will be the x and y components. The original vector can be represented alternatively by its length and the angle it makes with the x- axis.    The components of vector can be represented as multiples of unit vectors called I and j.The same vector can be represented by a different i* and j* unit vectors. This change  in characterisation of a vector is called change in basis; the vector total magnitude and angle remains unchanged.Change in basis is achieved by projection of components of a vector to the unit vectors of new basis. Projection is thus basically how much the component aligns in the new dir...

 ORGANIZATION: THE FRAMEWORK OF SOCIETY PART 3  Economic crisis in the developed world The western economies went in severe recession in 1929. In a market economy while wages are fully consumed the same is not true of profits. Profits require fresh investments provided workers have rising wages or new employment. Due to income inequality .which kept on growing in early twentieth century the workers wages were inadequate to buy products from new investment. What was needed was transfer of wealth to workers . However at this time world wars took place. This immediately increased production of armaments in new factories by government leading to new jobs and money to overcome the recession. War led to destruction of wealth of large capitalist and again reduced wealth and income gap. Post war Keynesian economics was adopted where govt taxes were used to create infrastructure projects creating new employment and purchasing power in workers.Govt investment had a multiplier effect in ...

 ORGANIZATION: THE FRAMEWORK OF SOCIETY PART 2 Medieval organizations After the collapse of Roman Empire a new type of organization arose, the feudal system. In the feudal system the feudal lord owned many serfs. Serfs were required to work for free in Lords land .Rest of the time he could work on his own land. He was also supposed to give military service when called for. He was free to marry ut was not allowed to leave his Feudal lord. The system was better than direct slavers as it gave some initiative to individual serfs to produce on his own land.     Alongside the feudal system was the Church with its hierarchical system of priests,with the Pope at the top. The church worked by persuasion to adhere to the religious code. But it also had vast land wealth and even a military. There were clashes between church and kings over the exercise of power.    The last organization was of craftsmen and traders. They usually lived in cities in organizations called ...

PHYSICS: ORIGIN OF ORGANISATIONS The second law of thermodynamics According to the second law entropy of the universe has to always increase. Entropy is a measure of random motion,such as heat.It is defined as dQ/ dT or quantity of heat in a system divided by its temperature. The importance of this formula is that spontaneous events take place only if there is an increase in entropy of the system,such as temperature is less in new state or quantity of heat is more.      At the origin of universe there was extremely high temperature and heat. This high energy allowed union of all four basic forces of nature ,gravity ,nuclear and electromagnetic. Thus even fermions and boson particles could not exist independently.        As the universe expanded a heat sink arose which allowed temperature to be less. This led  to a break in symmetry and separation of the forces of nature. Thus various fundamental particles could exist now at the lower temperature a...

ORGANIZATION: THE FRAMEWORK OF SOCIETY PART -1 The framework of society Power is the ability to control another persons decisions. It can be achieved by three means: physical intimidation,offering compensation and creating a conditioned response due to habit/ societal conformity.These are combined in various ways to create organizations . A conditioned response usually originates in a magnetic personality who creates a system of rules involving monetary/ hierarchical compensation system.In some organizations however the major glue is physical intimidation ( criminal gangs). Another example is the church which originated with the captivating personality of Jesus Christ and his followers. Here the rules of church were accompanied by the extensive property it owed. There was moreover the threat of punishment in the next world for heresy. One characteristic of organization is that the strength and reliability of its external power depends on the strength of its internal submission. An orga...