1. INTRODUCTION OF THE MATRIX INVERSION METHODS
1.1 MATRIX :- • A matrix is defined as an ordered rectangular array of numbers.
• A matrix is a system in which m.n elements are arranged in a rectangular formation of m rows and n columns bounded by brackets [].
• This formation is sometimes more explicitly known as m by n matrix, and written as m*n matrix.
• Each of the numbers of this formation is called an element of the matrix.
• A matrix represented by a capital letter such as A, B, etc.
• Example :-
• Each element of the matrix is represented by the same lower-case letter with two suffixes.
• The first denotes the row and the second suffix denotes the column.
• The matrix A is denoted by
1.1.1 What is the Inversion of Matrix
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1.3.1 Matrix inversion method :-
There is mainly two types of matrix inversion methods :
1. Direct method Gauss elimination
2. Iterative method Gauss sedial
1) Gauss Elimination method :-
This method is based on the elimination of the unknowns.
In this methods matrix A of AX=B is reduced to an upper triangular matrix, from which the unknowns are found by the back sutitution method.
2) Gauss sedial method :-
This is the modified method of Gauss Jacobi method.
That is, the method of iteration will converge if in each equation of the given system, the absolute value of the largest coefficient is greater than the sum of the absolute values of all the remaining coefficients.
2. HISTROY OF THE MATRIX INVERSION METHODS
"Matrix" is the Latin word for womb, and it retains that sense in English.
It can also mean more generally any place in which something is formed or produced.
The history of matrices goes back to ancient times! But the term "matrix" was not applied to the concept until 1850.
The origins of mathematical matrices lie with the study of systems of simultaneous linear equations.
The term "matrix" for such arrangements was introduced in 1850 by James Joseph
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"Methods of rectangular arrays," in which a method is given for solving simultaneous equations using a counting board that is mathematically identical to the modern matrix method of solution outlined by Carl Friedrich Gauss (1777-1855), also known as Gaussian elimination.
3. DERIVATION OF THE MATRIX INVERSION METHODS
3.1 Some steps of the matrix inversion methods :- o Say that you know Matrix A and B, and want to find Matrix X:
XA = B o It would be nice to divide both sides by A (to get X=B/A), but remember we can't divide. o But what if we multiply both sides by A-1 ?
XAA-1 = BA-1 o And we know that AA-1 = I, so:
XI = BA-1 o We can remove I (for the same reason we could remove "1" from 1x = ab for numbers):
X = BA-1 o And we have our answer (assuming we can calculate A-1)
Matrix the order of multiplication usually changes the answer. Do not assume that AB=BA, it is almost never
The actual “matrix” described in the movie The Matrix provides the best example of a matrix. The “matrix” in the movie is a virtual reality implemented and created by machines to use human beings as a power supply. Their minds are trapped and they are unaware of the reality that they are simply batteries for the machines. Matrices are situations or surrounding circumstances within which something else originates, develops, or is contained. For example, in the explanation of the matrix above, human beings are in the matrix and their minds are contained within that matrix. However, containment is not the only type of matrix. Many different matrices exist in our lives. The educational system at California State University, Northridge can be considered a matrix. When students attend the university they start as one person, and through education and social experiences a new person is developed. Dick’s novel and The Matrix contain in their stories many mat...
entertainment, and countless others. All of these matrices are related with each other and with specific operations of individuals. The book and the movie demonstrate the interaction of multiple matrices, from single to multi-dimesional. It shows the destruction and the development of systems and the impact of one individual on the largest matrix, the human race.
Bernardin, Marc. "The Matrix" 1999. <http://www.ew.com/ew/review/video/0,1683,846,matrix.html> (14 Apr. 2000) [address has moved to: <http://www.ew.com/ew/article/review/video/0,6115,270871~2|7696||0~,00.html> link updated by Dr P. 30 Oct 2002]
The Matrix series is much more than an action-packed sci-fi thriller. After one view of this film for the second and third time, we start to notice a great deal of symbolism. This symbolism starts to paint a completely different picture than the images of humans battling machines. It is a religious story, with symbols deeply set in the Christian faith. The Matrix contains religious symbolism through its four main characters, Morpheus, Neo, Trinity and Cypher. In that each character personifies the “Father,” the “Son,” “Satan,” and the “Holy Spirit” of the Christian beliefs only shown through the amazing performances of the actors. A critic by the name of Shawn Levy said "The Matrix slams you back in your chair, pops open your eyes and leaves your jaw hanging slack in amazement."(metacritic.com)
The 1999 film, The Matrix, shows many philosophical instances. Comparing this film to Plato’s The Republic: The Allegory of the Cave, and Descartes’ First Meditation on Philosophy allows one to gain a deeper understanding of the work. Reality is a concept that may be vague to many people due to their given circumstances. The environment and the mind a person is in allows for different perceptions of reality. The power of reality falls in the eyes of the beholder. As shown in The Matrix, Neo was not the One until he believed he was, which can percept into everyday life; how someone thinks can affect how someone is.
In this paper, I will be describing the theme of the demiurge which appears in The Matrix by the Wachowski Brothers and in the story “The Circular Ruins” by Jorge Luis Borges. In doing this I will develop an argument about it, and interpret it in the two texts in detail. I will also compare the visual text with the literary text, as well as talk about what writing can do that film cannot and vice versa. I will also cover how the artist use their respective media.
an initial value that is close to the root could result in finding a the wrong
• I will point to an empty space on the matrix and ask, “What will the rectangle for this space look like?, What equation will you write on it”?
and equimultiple n is taken of c and d, then a and b are in same ratio with c
Wigner, Eugene P. 1960. The Unreasonable Effectiveness of Mathematics. Communications on Pure and Applied Mathematics 13: 1-14.
order to solve a given problem, we have to solve di erent parts of the problem
There is always room in mathematics, however, for imagination, for expansion of previous concepts. In the case of Pascal’s Triangle, a two-dimensional pattern, it can be extended into a third dimension, forming a pyramid. While Pascal himself did not discover nor popularize it when he was collecting information on the Triangle in the 17th century, the new pattern is still commonly called a Pascal’s Pyramid. Meanwhile, its generalization, like the pyramid, to any number of dimensions n is called a Pascal’s Simplex.
whereβ the intercept 0 and β the slope 1 are unknown constants and ε is a random error component .
The dates regarding the advent of Mathematical Physics vary just as how the dates concerning the advent of Mathematics and Physics vary from person to person and from tale to tale. There is an account which says that the methods of Mathematical Physics as a theory of mathematical model in Physics can be traced in the works of Newton and his contemporaries such as Lagrange, Euler, Laplace, Gauss and others who contributed in the advancement of methods of Mathematical Physics. However, there is a version especially that of which written in The Evolution of Mathematical Physics (1924) by Lamb laying the mark of its birth in 1807; the date after the French Revolution had subsided and later succeeded by the relative tranquility of the early empire, and the year when Laplace, Lagrange, and several other mathematicians used Newton’s scientific work to model, describe and predict the motion of celestial and terrestrial bodies. In this age, the methods of Mathematical Physics were successfully used in studying mathematical models of physical phenomena. These models have something to do with electrodynamics, acoustics, theory of elasticity, hydrodynamics, aerodynamics, and other related areas. The models used were usually described using partial differential equation, integral and integrodifferential equations, variational and probability theory methods, potential theory, the theory of functions of complex variable. Some of the dominant western mathematicians and scientist who succeeded in studying and describing the physical world by mathematical modeling are Lord Kelvin, George Stokes, James Clerk Maxwell, and Guthrie Tait.
Linear algebra is the study of linear transformations of linear equations which are represented in a matrix form by matrices acting on vectors. Eigenvalues, eigenvectors and Eigen space are properties of a matrix (Sharma, n.d.). The prefix “Eigen” which means “proper” or “characteristics” was originally developed in German and invented by a German mathematician. Latent roots, characteristic roots, proper values or characteristics value are few common terms of eigenvalues. They are a special set of scalars allied with a linear system of equations for instance a matrix equation. In engineering and physics field, knowledge about eigenvalues and eigenvectors are very crucial where it is corresponding to diagonalization of matrix. They are practice in vibrating system with small oscillations, concepts of rotating bodies, as well as stability analysis. Corresponding eigenvectors will be paired with their eigenv...