Define Matrix Theory and Different Types of Matrixes

matrix theory and types of matrices

Matrix theory is important in a variety of scientific researches. It have been used in different areas of Physics, including classical mechanics, optics and quantum mechanics. The study of matrices also been used to investigate few physical phenomena, such as motion of rigid bodies. Also, in computers graphics have been used for developing 3-D models and projecting them on onto 2-D surfaces.

What is the Gram Schmidt Procedure? Explanation and Example

gram schmidt procedure demonstration

Since, by applying head to tail rule on the vectors components, we can generate the original vector A. After that we need to find the projections of one vector to another vector. This projection is subtracted from the other vector and hence these two vectors become orthogonal.

So, for two vectors A and B lets say we want to generate a new set of vectors W and Y that will be orthogonal to each other. We will assume

Define Cryptic Mining for Automatic Variable Key-based Cryptosystem

The AVK method is useful for low-power secure device communication, which is a key element of the internet of things. This paper examines and analyses the state of symmetric cryptosystems as well as the evolution of automatic variable key cryptosystems. It explains the framework of the AVK model and how to extend it using a parameterized method.

What are the sequences and arithmetic progressions?

sequences an arithmetic mean

If the numbers are generated according to a certain rule such that each consecutive number has a specific relation with its neighbors then they are said to form a sequence. You can consider sequences as list of ordered pairs. Sequences are represented by {an} where n is an integer. The value of n can be any integer or from natural number (1,2,3,….) which is called the domain of sequence. Each number in the sequence is called term.

Gram Schmidt Orth-normalization Based Projection Depth

Gram Schmidt Orthonormalization

GSO (Gram-Schmidt Orth normalization) is based on depth function of Euclidean vector which can be proposed to compute the projection depth. The performance of GSO can be studied to exact and approximate algorithms, bivariate data (data from two variables) can be used to associate estimation namely Stahel-Donoho (S-D) location and scatter estimation. The efficiency can be checked by computing average misclassification error in discriminant analysis under real and stimulating environment.

Application of Linear Algebra in Computer Graphics

application of linear algebra in computer graphics

The first use of Linear Algebra can be seen in the polygonal structure of 3D characters and space in computer games and other 3D graphics applications. Polygons are used to make images look three-dimensional because of their geometric structures. Most of the time, this is done by dividing the object into smaller and smaller polygons where the given smaller parts are triangular. This makes the production of 3D objects part of the distribution process of polygons. A simple example of the use of polygons in 3D images in the form of object frame.

What is the machine epsilon?

machine epsilon

What is the machine epsilon? Computer systems are the digital systems. Every information that is represented in computer is always limited in its representation in terms of the number of bits available. Every machine (calculator, computer) has specific number of bits reserved for representing a number. Real numbers are represented as floats in computers. There are two ways for representing real numbers in computers:

What is the method of false position? Drive formula of it.

false position method error

This is one of the iterative methods that give you the root if the function changes its sign: from positive to negative or from negative to positive. Despite the fact that bisection is an entirely legitimate strategy for determining roots, its “brute force” approach is generally inefficient. False position is based on graphical approach. A shortcoming of the bisection method is that, in dividing the interval from xl to xu into equivalent parts, no record is taken of the values of f (xl) and f (xu).