Computer Science
Matrix Operations in C
Matrix operations in C involve performing various mathematical operations on matrices using the C programming language. These operations can include addition, subtraction, multiplication, and transposition of matrices. By using C, programmers can efficiently manipulate and process matrices to perform tasks such as solving systems of linear equations, implementing algorithms for image processing, and conducting scientific computations.
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4 Key excerpts on "Matrix Operations in C"
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
Matrices find many applications. Physics makes use of matrices in various domains, for example in geometrical optics and matrix mechanics; the latter led to studying in more detail matrices with an infinite number of rows and columns. Graph theory uses matrices to keep track of distances between pairs of vertices in a graph. Computer graphics uses matrices to project 3-dimensional space onto a 2-dimensional screen. Matrix calculus generalizes classical analytical notions such as derivatives of functions or exponentials to matrices. The latter is a recurring need in solving ordinary differential equations. Serialism and dodecaphonism are musical movements of the 20th century that use a square mathematical matrix to determine the pattern of music intervals. A major branch of numerical analysis is devoted to the development of efficient algorithms for matrix computations, a subject that is centuries old but still an active area of research. Matrix decomposition methods simplify computations, both theoretically and practically. For sparse matrices, specifically tailored algorithms can provide speedups; such matrices arise in the finite element method, for example. Definition A matrix is a rectangular arrangement of numbers. For example, An alternative notation uses large parentheses instead of box brackets: The horizontal and vertical lines in a matrix are called rows and columns , respectively. The numbers in the matrix are called its entries or its elements . To specify the size of a matrix, a matrix with m rows and n columns is called an m -by-n matrix or m × n matrix, while m and n are called its dimensions . The above is a 4-by-3 matrix. ________________________ WORLD TECHNOLOGIES ________________________ A matrix with one row (a 1 × n matrix) is called a row vector, and a matrix with one column (an m × 1 matrix) is called a column vector.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
Matrices find many applications. Physics makes use of matrices in various domains, for example in geometrical optics and matrix mechanics; the latter led to studying in more detail matrices with an infinite number of rows and columns. Graph theory uses matrices to keep track of distances between pairs of vertices in a graph. Computer graphics uses matrices to project 3-dimensional space onto a 2-dimensional screen. Matrix calculus generalizes classical analytical notions such as derivatives of functions or exponentials to matrices. The latter is a recurring need in solving ordinary differential equations. Seria-lism and dodecaphonism are musical movements of the 20th century that use a square mathematical matrix to determine the pattern of music intervals. A major branch of numerical analysis is devoted to the development of efficient algori-thms for matrix computations, a subject that is centuries old but still an active area of research. Matrix decomposition methods simplify computations, both theoretically and practically. For sparse matrices, specifically tailored algorithms can provide speedups; such matrices arise in the finite element method, for example. Definition A matrix is a rectangular arrangement of numbers. For example, An alternative notation uses large parentheses instead of box brackets: The horizontal and vertical lines in a matrix are called rows and columns , respectively. The numbers in the matrix are called its entries or its elements . To specify the size of a matrix, a matrix with m rows and n columns is called an m -by-n matrix or m × n matrix, while m and n are called its dimensions . The above is a 4-by-3 matrix. ________________________ WORLD TECHNOLOGIES ________________________ A matrix with one row (a 1 × n matrix) is called a row vector, and a matrix with one column (an m × 1 matrix) is called a column vector.
- Jose M. Garrido(Author)
- 2013(Publication Date)
- Chapman and Hall/CRC(Publisher)
Chapter 18 Matrices and Sets of Linear Equations 18.1 Introduction As mentioned in previous chapters, in scientific computing, data is conveniently organized as collections of values known as vectors and matrices and are used to implement data lists and sequences of values. This chapter presents basic concepts of matrices, programming in C and the GSL, and a summary of computing with matrices. Systems of linear equations are solved using the GSL. 18.2 Matrices In general, a matrix is a two-dimensional array of data values and is organized in rows and columns. The following array, Y , is a two-dimensional array organized as an m × n matrix; its elements are arranged in m rows and n columns. Y = y 11 y 12 ··· y 1 n y 21 y 22 ··· y 2 n . . . . . . . . . . . . y m 1 y m 2 ··· y mn The first row of Y consists of elements: y 11 , y 12 ,..., y 1 n . The second row consists of elements: y 21 , y 22 ,..., y 2 n . The last row of Y consists of elements: y m 1 , y m 2 ,..., y mn . In a similar manner, the elements of each column can be identified. 18.2.1 Basic Concepts A matrix is defined by specifying the rows and columns of the array. An m by n matrix has m rows and n columns. A square matrix has the same number of rows and columns, n rows and n columns, which is denoted as n × n . The following example shows a 2 × 3 matrix, which has two rows and three columns: 235 236 Introduction to Computational Modeling 0 . 5000 2 . 3500 8 . 2500 1 . 8000 7 . 2300 4 . 4000 A matrix of dimension m × 1 is known as a column vector and a matrix of di-mension 1 × n is known as a row vector . A vector is considered a special case of a matrix with one row or one column. A row vector of size n is typically a matrix with one row and n columns. A column vector of size m is a matrix with m rows and one column.
eBook - PDF- C Y Hsiung, G Y Mao(Authors)
- 1998(Publication Date)
- World Scientific(Publisher)
CHAPTER 3 MATRIX OPERATIONS The concept of matrices was discussed in the previous chapter. It is not only an important tool for treating a system of linear equations, but also an indispensable tool for studying linear functions. In the following chapters we shall often make use of it. The advantage of matrix operations is that when a matrix is regarded as a quantity, it makes operations on arrays of ordinary numbers extremely simple. In this chapter we shall discuss matrix operations, particularly as regards the following three aspects. 1. Matrix addition, matrix subtraction, scalar multiplication, matrix multipli-cation, etc., as well as the basic properties of these matrix operations. 2. Some specially important matrices. 3. The necessary and sufficient condition for a matrix to be invertible and methods of finding an inverse matrix. This chapter is divided into three parts in which we in turn consider the above three aspects. 3.1. Matrix Addition and Matrix Multiplication In Sec. 2.1 the definition of a matrix was given. The matrix A of order n is called a nonsingular matrix if its determinant A ^ 0. Otherwise, i.e., A = 0, A is called a singular matrix. When all elements are real numbers, A is called a real matrix. As in the case of equality, addition, scalar multiplication of vectors, we have the following definitions. 92
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