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# Topic: Matrix (mathematics)

 Mathematics It is based on a philosophy of teaching and learning mathematics that is consistent with the current research, exemplary practices, and national standards. The North Carolina Mathematics Standard Course of Study is organized in five strands or goals for K-8: Number and Operations, Measurement, Geometry, Data Analysis and Probability, and Algebra. The Standard Course of Study describes the mathematical concepts, skills, operations, and relationships that are the significant mathematics that all North Carolina students should learn and understand. www.dpi.state.nc.us /curriculum/mathematics   (276 words)

 Matrix (mathematics) Summary In an identity matrix, all elements are 0 except the diagonal elements that are all equal to 1. The entry of a matrix A that lies in the i -th row and the j-th column is called the i,j entry or (i,j)-th entry of A. The rank of a matrix A is the dimension of the image of the linear map represented by A; this is the same as the dimension of the space generated by the rows of A, and also the same as the dimension of the space generated by the columns of A. www.bookrags.com /Matrix_(mathematics)   (3268 words)

 Matrix (mathematics) Encyclopedia   (Site not responding. Last check: ) A 1 × n matrix (one row and n columns) is called a row vector, and an m × 1 matrix (one column and m rows) is called a column vector. The rank of a matrix A is the dimension of the image of the linear map represented by A; this is the same as the dimension of the space generated by the rows of A, and also the same as the dimension of the space generated by the columns of A. The trace of a square matrix is the sum of its diagonal entries, which equals the sum of its n eigenvalues. www.hallencyclopedia.com /topic/Matrix_(mathematics).html   (1959 words)

 Matrix (mathematics) - Wikipedia, the free encyclopedia The entry of a matrix A that lies in the i -th row and the j-th column is called the i,j entry or (i,j)-th entry of A. A 1 × n matrix (one row and n columns) is called a row vector, and an m × 1 matrix (one column and m rows) is called a column vector. The rank of a matrix A is the dimension of the image of the linear map represented by A; this is the same as the dimension of the space generated by the rows of A, and also the same as the dimension of the space generated by the columns of A. en.wikipedia.org /wiki/Matrix_(mathematics)   (1669 words)

 Matrix theory - Wikipedia, the free encyclopedia Matrix theory is a branch of mathematics which focuses on the study of matrices. Therefore matrix theory is usually considered as a branch of linear algebra. A permutation matrix is the matrix representation of a permutation; it is a square matrix with entries 0 and 1, with just one entry 1 in each row and each column. en.wikipedia.org /wiki/Matrix_theory   (291 words)

 matrix (mathematics) In mathematics, a square (n × n) or rectangular (m × n) array of elements (numbers or algebraic variables) used to facilitate the study of problems in which the relation between the elements is important. The size of a matrix is described by stating the number of its rows and then the number of its columns so, for example, a matrix with three rows and two columns is a 3 × 2 matrix. A matrix with equal numbers of rows and columns is called a ‘square matrix’. www.tiscali.co.uk /reference/encyclopaedia/hutchinson/m0006702.html   (370 words)

 AllRefer.com - matrix (Mathematics) - Encyclopedia matrix, in mathematics, a rectangular array of elements (e.g., numbers) considered as a single entity. A matrix having the same number of rows as columns is called a square matrix. Definitions are made for certain operations with matrices; for example, a matrix may be multiplied by a number, and two matrices of the same order may be added or multiplied using an algebra of matrices that has been developed. reference.allrefer.com /encyclopedia/M/matrix.html   (238 words)

 Matrix and Quaternion FAQ A matrix with M rows and N columns is defined as a MxN matrix. For all powers, the matrix must be square, that is orthogonal and the same width and height For example, -1 M is the inverse of the matrix 0 M generates the identity matrix 1 M leaves the matrix unchanged. The inverse of an identity matrix is the identity matrix. www.j3d.org /matrix_faq/matrfaq_latest.html   (7736 words)

 Matrix Inverse Calculator 1.0 - Uses a complicated method to find the inverse of any square matrix You simply choose your matrix's dimensions, and then enter the elements of the matrix you want inverted in the left frame. When you press Enter, the inverse matrix will be shown in the right frame. If your matrix doesn't have an inverse, you will be told so. www.downloadthat.com /windows/Educational/Mathematics/Matrix-Inverse-Calculator.html   (254 words)

 Bernstein, D.S.: Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory. Matrix Mathematics is a reference work for users of matrices in all branches of engineering, science, and applied mathematics. Hundreds of identities, inequalities, and matrix facts are stated rigorously and clearly with cross references, citations to the literature, and illuminating remarks. Twelve chapters cover all of the major topics in matrix theory: preliminaries; basic matrix properties; matrix classes and transformations; matrix polynomials and rational transfer functions; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; norms; functions of matrices and their derivatives; the matrix exponential and stability theory; and linear systems and control theory. press.princeton.edu /titles/8009.html   (359 words)

 MTH-2B71 : Mathematics for Geophysical Science I This unit is the pre-requisite for Mathematics for Geophysical Science II, studied in the Spring. Mathematics for Geophysical Science I is taught by lectures and seminars, and computer laboratory sessions. This unit covers matrix algebra for the solution of systems of linear equations and Markov chain modelling of competing populations. www.mth.uea.ac.uk /maths/syllabuses/0506/2B7105.html   (556 words)

 Matrix (mathematics) - Simple English Wikipedia In mathematics, a matrix (plural matrices) is a rectangular table of numbers. The sum of two matrices is the matrix, which (i,j)-th entry is equal to the sum of the (i,j)-th entries of two matrices: the product is a matrix with the same number of rows as the first matrix and the same number of columms as the second matrix. simple.wikipedia.org /wiki/Matrix_(math)   (329 words)

 Matrix (mathematics) at opensource encyclopedia   (Site not responding. Last check: ) In mathematics, a matrix (plural matrices) is a rectangular table of numbers or, more generally, of elements of a fixed ring. The entry of a matrix A that lies in the ith row and the j-th column is called the i,j-entry or (i,j)th entry of A. A partitioned matrix or block matrix is a matrix of matrices. www.wiki.tatet.com /Matrix_(mathematics).html   (1636 words)

 83.07.04: Computed Tomography and Nuclear Magnetic Resonance with Mathematical Applications Mathematics studied in the secondary mathematics curriculum will be developed and how the mathematics applies to both computed tomography and nuclear magnetic resonance will be discussed. The fineness of the matrix refers to the number of picture elements in the matrix (pixels) and is expressed by giving the number of picture elements along each axis of the grid (examples 80 x 80, 160 x 160). For example, the solutions of a 4 x 4 matrix and a 6 x 6 matrix are not similar because 4 is a multiple of both 2 and 4 while 6 is a multiple of 2,3 and 6. www.yale.edu /ynhti/curriculum/units/1983/7/83.07.04.x.html   (5124 words)

 ONLamp.com -- Numerical Python Basics The second example is a 1-by-2 matrix multiplied by a 2-by-1 matrix resulting in a 1-by-1 matrix (also known as a scalar). Matrix division is undefined; the concept is replaced by the matrix inverse. When a matrix and its inverse are multiplied together, the result is the identity matrix or I. The identity matrix is a square matrix where all elements are 0 except along the main diagonal (going from upper left to lower right). www.onlamp.com /pub/a/python/2000/05/03/numerically.html?page=1   (832 words)

 Mathematics Major, Mathematics Department USNA The mathematical challenges facing the twenty-first century Navy touch a vast number of sub-disciplines in mathematics, from the traditional applied math subjects of numerical analysis, engineering mathematics, operations research, and statistics to problems applying discrete math, algebra, and algebraic geometry. Mathematics Track - The Mathematics Track offers more background in theory and foundations of mathematics, with courses in the traditional areas of analysis, linear algebra, complex variables, algebra, topology, geometry, and combinatorics, applications such as cryptography and coding theory, and special topics courses such as differential geometry, algebraic geometry, and mathematical physics. Recent mathematics majors have earned Master degrees through VGEP studies at the George Washington University, George Mason University, and the University of Maryland, while IGEP participants have continued their mathematical studies at MIT, the University of Pennsylvania, the University of Wisconsin, and the University of Chicago Business School. www.usna.edu /MathDept/website/MathMajor.html   (590 words)

 Matrix (JScience v3.3 API) Indicates if this matrix can be considered equals to the one specified using the specified comparator when testing for element equality. It is the value obtained by evaluating the determinant formed by the elements not in that particular row or column. The vectorization of a matrix is the column vector obtain by stacking the columns of the matrix on top of one another. jscience.org /api/org/jscience/mathematics/vectors/Matrix.html   (818 words)

 SDE: Mathematics Mathematics Curriculum Guide CD Rom files, developed with GOALS 2000 funding by EASTCONN in collaboration with the Connecticut State Department of Education, are now available on this web site. Components are designed to assist districts in their development of a local mathematics curriculum guide. The focus of this organization is to improve student interest in mathematics and their ability to problem solve through competitions for middle grades and high school students. www.sde.ct.gov /sde/cwp/view.asp?a=2618&q=320872   (838 words)

 Dr. Matrix at the Scientium: Mathematics Links   (Site not responding. Last check: ) CAMSED - Coalition of Automated Mathematics and Science Education Databases - The Coalition of Automated Mathematics and Science Education Databases (CAMSED) is an emerging collaborative effort, striving to increase access to materials useful to individuals in the mathematics and science education community through a system of federated electronic information services. Mathematical Mayhem is a non-profit mathematical journal written by and for high school and undergraduate university students. The mathematical basis for the Mercator projection is an 1851 law of geometry known as the Riemann mapping theorem (although the 16th-century cartographer himself wasn't aware of it, of course). www.scientium.com /drmatrix/sciences/math.htm   (1411 words)

 Matrix (mathematics) -   (Site not responding. Last check: ) Matrices are useful to record data that depend on two parameters, and to keep track of the coefficients of systems of linear equations and linear transformations. The identity matrix is the identity element in the ring of square matrices. Excel add-ins for Matrix Algebra and Extended Precision functions These are freeware, open source. psychcentral.com /psypsych/Matrix_(mathematics)   (2029 words)

 [No title] Matrix analysis is a more advanced version of the linear algebra course that mathematics majors typically take in their first or second year of college. We say that an m-by-n matrix B is semipositive provided there is an entry-wise nonnegative n-vector x (i.e., every entry of x is greater than or equal to zero) such that the m-vector Bx is entry-wise positive. Such matrices arise in the study of convergence of matrix sets and we know that a certain subclass of the semipositive matrices, namely the class of minimally semipositive matrices, is particularly important. www.math.wm.edu /~lutzer/anncment.html   (2598 words)

 matrix - Definitions from Dictionary.com Mathematics A rectangular array of numeric or algebraic quantities subject to mathematical operations. Bone cells are embedded in a matrix of collagen fibers and mineral salts. The name of the rather good 1999 cypherpunk movie "The Matrix" played on this sense, which however had been established for years before. dictionary.reference.com /browse/matrix   (1446 words)

 mkaz.com : Java Matrix Calculator Updated so it accepts any rectangular matrix for the transpose and also for multiplication if matrices A and B are appropriate size (ie 2x3 3x5 are acceptable for multiplication and produce a 2x5 matrix) The calculation of the determinant, by definition, is based upon a factorial number of calculations with respect to the size of the matrix. The determinant of A-transpose equals the determinant of A. If the matrix B is constructed by interchanging two rows (columns) in matrix A, then the determinant of B equals the negative determinant of A www.mkaz.com /math/matrix.html   (469 words)

 Matrix (mathematics)   (Site not responding. Last check: ) Matrices are useful to record data that depend on two categories, and to keep track of the coefficients of systems of linear equations and linear transformations. A matrix with m rows and n columns is called an m-by-n matrix (or mÃ—n matrix) and m and n are called its dimensions. Multiplication of two matrices is well-defined only if the number of columns of the first matrix is the same as the number of rows of the second matrix. www.pillscatalog.net /Matrix_%28mathematics%29.html   (1952 words)

 Mathematics HQ : Matrix Mathematics Non-fiction with an emphasis on mathematics at undergraduate, graduate and researchlevel. AAda95 Matrix Package First Release, August 1996 The archive of this matrixpackage is available in the compressed tar format, or in the zip format. Mathematics HQ excludes all liability of any kind (including negligence) in respect of any third party information or other material made available on, or which can be accessed using, this Website. mathematicshq.com /matrixmathematics/index.php   (665 words)

 MathEduSoft   (Site not responding. Last check: ) Advantix Calculator can be used as a powerful and easy-to-use scientific calculator that supports all mathematical operations on real and complex numbers (collectively known as scalar numbers). Advantix Calculator supports all common mathematical operations on integers that are represented in one of the following bases: binary (base 2), octal (base 8), decimal (base 10) or hexadecimal (base 16). Matrix Function is a function that returns a matrix. advantix.350nice.com /sc00001.htm   (1087 words)

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