Properties of matrices
1 Properties of matrices In this section, we review some basic concepts of matrix theory and some fundamental properties of matrices, focusing on those that will be needed in later sections. Matrices and vectors A matrix is a rectangularCiteste tot ... 2260 cuvinte
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Solving systems of linear equations
Solving systems of linear equations Solving a set of simultaneous linear equations is a fundamental problem that occurs in diverse applications. A linear system can be expressed as a matrix equation in which each matrix or vector element belCiteste tot ... 3092 cuvinte
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Symmetric positive-definite matrices and least-squares approximation
Symmetric positive-definite matrices and least-squares approximation Symmetric positive-definite matrices have many interesting and desirable properties. For example, they are nonsingular, and LU decomposition can be performed on them without oCiteste tot ... 4922 cuvinte
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Computational geometry
COMPUTATIONAL GEOMETRY Computational geometry is the branch of computer science that studies algorithms for solving geometric problems. In modern engineering and mathematics, computational geometry has applications in, among other fields, cCiteste tot ... 10127 cuvinte
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Inverting matrices
Inverting matrices Although in practice we do not generally use matrix inverses to solve systems of linear equations, preferring instead to use more numerically stable techniques such as LUP decomposition, it is sometimes necessary to compuCiteste tot ... 1276 cuvinte
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Polynomials and the fft
POLYNOMIALS AND THE FFT The straightforward method of adding two polynomials of degree n takes (n) time, but the straightforward method of multiplying them takes (n2) time. In this chapter, we shall show how the Fast Fourier Transform, or FFT,Citeste tot ... 6528 cuvinte
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Strassen's algorithm for matrix multiplication
Strassen's algorithm for matrix multiplication This section presents Strassen's remarkable recursive algorithm for multiplying n n matrices that runs in (nlg 7) = O(n2.81) time. For sufficiently large n, therefore, it outperforms the naiveCiteste tot ... 1234 cuvinte
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Number-theoretic algorithms
NUMBER-THEORETIC ALGORITHMS Number theory was once viewed as a beautiful but largely useless subject in pure mathematics. Today number-theoretic algorithms are used widely, due in part to the invention of cryptographic schemes based on large prCiteste tot ... 17520 cuvinte
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Linear algebra – theorems
LINEAR ALGEBRA – THEOREMS 1.1 A homogeneous system of m equations in n variables either has a unique solution (zero solution) or has infinitely many solutions, deCiteste tot ... 1649 cuvinte
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Conics - a class of plain curves
C O N I C S Conics reprezent a class of plain curves with special properites, which have numerous applications in various domains. The mathematicians of the elenic era obtained non-degenerated conics by the intersection of a rotatiCiteste tot ... 5507 cuvinte
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Trigonometry - Maths Extension
Trigonometry Ø Trigonometric Ratios Ø Exact Values & Triangles Ø Trigonometric Identities Ø ASTC Rule Ø &Citeste tot ... 4741 cuvinte
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Geometrical Characteristics of the Beam Cross-Section
Geometrical Characteristics of the Beam Cross-Section The definitions of the beam and cross-section were specified in the previous lectures. Some geometrical characteristics of the cross-section, such as the area and moments of inerCiteste tot ... 2369 cuvinte
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Complex Numbers
Complex Numbers The beauty of physics and mathematics is that everything is somehow related to everything else, and that there are so many ways of looking at the same thing, each providing new insights. Take for instance the Fourier transform.Citeste tot ... 1379 cuvinte
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Mathematical Model of the OFDM Signal
Mathematical Model of the OFDM Signal In order to perform the mathematical analysis of OFDM signals, the most convenient strategy is to use the signal theory related to the orthogonal expansion of signaCiteste tot ... 3273 cuvinte
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A DIFFERENT DEMONSTRATION OF THE PYTHAGOREAN THEOREM USING THE POWER OF THE POINT WITH RESPECT TO A CIRCLE
A DIFFERENT DEMONSTRATION OF THE PYTHAGOREAN THEOREM USING THE POWER OF THE POINT WITH RESPECT TO A CIRCLE In the present paper I will give / offer you not only a different demonstration of the Pythagorean Theorem but alsoCiteste tot ... 988 cuvinte
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Maths and Vibrations – Tutorial Sheet 4
Maths and Vibrations – Tutorial Sheet 4 1) Find the limit of the following functions as x tends to zero, i) ii) iii) 2) Differentiate the following equations with respeCiteste tot ... 86 cuvinte
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Maths and Vibrations – Tutorial Sheet 2
Maths and Vibrations – Tutorial Sheet 2 1) Sketch the functions sin(x), cos(x) and tan(x) and also cosec(x), sec(x) and cot(x) between -p and p. Note the angles where they cross the axes and indicate any asymptotes. Which are odd or even fCiteste tot ... 126 cuvinte
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Maths and Vibrations: Tutorial Sheet 9 Solutions
Maths and Vibrations: Tutorial Sheet 9 Solutions 1) b) Inertia 2) b) (see course book part 2) 3) 4) 5) 6) Total eneCiteste tot ... 117 cuvinte
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Tutorial Sheet 7 Solutions
Tutorial Sheet 7 Solutions With most transforms simply refer to a table (e.g. page 57,58). 1) i) ii) iii) iv) Citeste tot ... 59 cuvinte
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Irish Maths Test
Irish Maths Test An Irishman wants a job, but the foreman won't hire him until he passes a little math test. Here is your first question, the foreman said. 'Without using numbers, represent the number 9.' 'WCiteste tot ... 268 cuvinte
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