Principal diagonal
In linear algebra, the main diagonal (sometimes leading diagonal or major diagonal or primary diagonal or principal diagonal) of a matrix A is the collection of entries A_{i,j} where i is equal to j.
The main diagonal of a square matrix is the diagonal which runs from the top left corner to the bottom right corner. For example, the following matrix has 1s down its main diagonal:
\begin{bmatrix}<br />
1 & 0 & 0\\<br />
0 & 1 & 0\\<br />
0 & 0 & 1\end{bmatrix}.
A square matrix like the above in which the entries outside the main diagonal are all zero is called a diagonal matrix. The sum of the entries on the main diagonal of a square matrix is known as the trace of that matrix.
The main diagonal of a rectangular matrix is the diagonal which runs from the top left corner and steps down and right, until the right edge or the bottom edge is reached.
\begin{bmatrix}<br />
1 & 0 & 0 & 0 \\<br />
0 & 1 & 0 & 0 \\<br />
0 & 0 & 1 & 0 \end{bmatrix}
\begin{bmatrix}<br />
1 & 0 & 0\\<br />
0 & 1 & 0\\<br />
0 & 0 & 1\\<br />
0 & 0 & 0\end{bmatrix}
The diagonal of a square matrix from the top right to the bottom left corner is called antidiagonal, counterdiagonal, secondary diagonal, or minor diagonal.

This is an excerpt from the article Principal diagonal from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
The article Principal diagonal at en.wikipedia.org was accessed 28 times in the last 30 days. (as of: 06/11/2013)
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Main diagonal - Wikipedia, the free encyclopedia
In linear algebra, the main diagonal (sometimes leading diagonal or major diagonal or primary diagonal or Principal diagonal) of a matrix A is the collection of ...
en.wikipedia.org/wiki/Main_diagonal
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principal diagonal - The Free Dictionary
The diagonal in a square matrix that goes from the upper left corner to the lower right corner. Thesaurus Legend: Synonyms Related Words Antonyms. Noun, 1 ...
www.thefreedictionary.com/principal+diagonal
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Principal Diagonal -- from Wolfram MathWorld
Principal diagonal. SEE: Diagonal. Wolfram Web Resources. Mathematica ». The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha » ...
mathworld.wolfram.com/PrincipalDiagonal.html
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Principal diagonal - Merriam-Webster Online
Definition of Principal diagonal. : the diagonal in a square matrix that runs from upper left to lower right. First Known Use of Principal diagonal. 1964 ...
www.merriam-webster.com/dictionary/principal%20diagonal
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Principal diagonal - FREEganita.com
The Principal diagonal elements (from top left corner to bottom right corner) of matrix A ... A matrix whose Principal diagonal elements are non zero and all other ...
www.freeganita.com/en/modmat/3_5.htm
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matlab - Selecting Principal Diagonal Elements - Stack Overflow
In the matrix shown below how can I select elements 01, 09, 17 and ... Use diag to get elements on the diagonal. diagA = diag(A). You can restrict ...
stackoverflow.com/questions/5714125/selecting-principal-diagonal-elements
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Principal diagonal | Define Principal diagonal at Dictionary.com
Principal diagonal definition, diagonal See more. ... upper left to lower right (main diagonal or Principal diagonal) or lower left to upper right (secondary diagonal) ...
dictionary.reference.com/browse/principal+diagonal
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Bounds for Determinants with Dominant Principal Diagonal - jstor
for determinants with dominant Principal diagonal (see a recent paper on these determinants by Olga Taussky [9 ] 2). The lower bound is an improvement of a ...
www.jstor.org/stable/2031782
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Principal Diagonal of a Square Matrix, Scalar Matrix and Identity ...
High School Mathematics Curriculum - Principal diagonal of a Square Matrix, Scalar Matrix and Identity Matrix - Math & English ...
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Interglot - "principal diagonal": Synonyms in English
Synonyms for "Principal diagonal" in English including definitions, and related words.
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Principal diagonal in science
main diagonal - The Free Dictionary
Information about main diagonal in the free online English dictionary and ... crossed the main square of the campus of Western Washington University using the ...
principal diagonal - The Free Dictionary
Pronunciation of Principal diagonal. ... Information about Principal diagonal in the free online English dictionary and encyclopedia. ... Princeton University ...
Estimating Invariant Principal Components Using Diagonal ...
Estimating Invariant Principal Components Using Diagonal Regression. University of Hertfordshire Research Archive. Help | UH Research Archive. UHRA Home ...
dict.cc dictionary :: principal diagonal [matrix] :: German-English ...
dict.cc German-English Dictionary: Translation for Principal diagonal [matrix] ... English-German translation for: Principal diagonal [matrix]. ä ö ü ß. DE EN, DE ...
Definition of principal diagonal in Oxford Dictionaries (US English ...
Principal diagonal definition, pronunciation, and example sentences in Oxford University Press (US English) (US)
principal diagonal, principal diagonals- WordWeb dictionary definition
Encyclopedia: Principal diagonal. Nearest. Princess Grace of Monaco · Princess of Wales · princess pine · princess royal · Princeton · Princeton University ...
[PDF]Diagonal Principal Component Analysis for Face Recognition
Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China. Abstract. In this paper, a novel subspace method called diagonal principal ...
What does principal diagonal mean? definition, meaning and ...
PRINCETON UNIVERSITY · PRINCETON WORDNET · PRINCEWOOD · PRINCIPAL · PRINCIPAL AXIS · Principal diagonal · Dictionary: go down ...
Matrix Algebra
A symmetric matrix has the property that elements above and below the main diagonal are the same such that element(i,j) = element(j,i), as in our matrix B. ( The ...
[PDF]On Matrices with Elements in a Principal Ideal Ring
DigitalCommons@University of Nebraska - Lincoln ... Indiana University. Follow this ... form [that is, with zeros below the main diagonal] is again in normal form.
Books on the term Principal diagonal
Computational Chemistry Using the PC
Computational Chemistry Using the PC
Donald W. Rogers, 2003
A diagonal matrix has nonzero elements only on the Principal diagonal and zeros elsewhere. ... Large matrices with small matrices symmetrically lined up along the Principal diagonal are sometimes encountered in computational chemistry.
Mathematics Class 9
Mathematics Class 9
Pearson
Principal diagonal of a square matrix: In a square matrix A of order n, the elements a (i.e., a , a22 , a ) constitute the Principal diagonal. The elements fl are called elements of Principal diagonal. Examples 1. A = 2 -3 4 5 The elements 2,5 (i.e., ...
Modern Factor Analysis
Modern Factor Analysis
Harry H. Harman, 1976
Introduction From basic mathematical theory it is known that a matrix of real numbers that is symmetric and is dominated by the Principal diagonal is positive semi-definite (i.e.. Gramian) with the important property of having all of its eigenvalues ...
Super Course in Mathematics for the IIT-JEE: Algebra II
Super Course in Mathematics for the IIT-JEE: Algebra II
Trishna Knowledge Systems
The diagonal containing the elements all, a22, a22. .. an“ is called its Principal diagonal. ... As an illustration, consider the square matrix A = 12' azs " 3 5 6 -1 2 3 l 8 0 5 IO 7 1 1 -1 3 The Principal diagonal of A consists of the elements 3, 3, ...
Matrices
Matrices
Dr. V.N. Kala, Rajeshri Rana, 2009
Here elements 7, 3, 12 of square matrix are called its diagonal elements and diagonal along which these elements tie is called Principal diagonal. In Square matrix, I = [a ,j] (a) For element lying along Principal diagonal we have i = j (b) For ...
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Principal diagonal
Matriz 3x3 - Diagonal Principal En Cero (0). ~ Full Programacion
Todo sobre programacion
fullprogramacion18.blogspot.com/2013/04/matriz-3x3-diagonal-principal-en-cero-0.html
Thoughts On Economics: Kalecki And Sraffa: Compatible?
Two Great Economists1. 0 Introduction Michal Kalecki set out macroeconomic models in which markup pricing was common.
robertvienneau.blogspot.com/2013/05/kalecki-and-sraffa-compatible.html
Matrices Triangulares
Una matriz triangular es un tipo de matriz cuadrada cuyos elementos por encima o por debajo de su diagonal principal son cero. En este video se explica este tipo especial de matrices En este video hablaremos sobre algunos tipos especiales de matrices. Recordemos que en videos anteriores habíamos definido la matriz identidad ( I_n) como la matriz en la cual la diagonal principal de la matriz estaba compuesta por valores de 1 y el resto de la matriz, es decir los elementos que no formaban parte de la diagonal principal adquirían valores de 0. Para dar una definición más formal del concepto de diagonal principal de una matriz, decimos que si tenemos una matriz A con varias entradas, la diagonal principal está conformada por el siguiente conjunto de valores: diagA={a11,a22,a33,….ann}, a partir de la definición de diagonal principal de una matriz surgen algunas otras definiciones, se dice que todo lo que está arriba de la diagonal principal de la matriz es conocido como parte triangular superior y que todo lo que está por debajo de la diagonal principal de la matriz se le conoce como parte triangular inferior. Basados en esta definición, podemos decir que si nos dan una matriz cuadrada A y la diagonal de esta matriz se define como diagA={1,1,1,..1}, es decir, todos los elementos de la diagonal valen1, y que además, todos los elementos aij =0 para i≠j, nuestra matriz A se trata de la matriz identidad A= I_n. Otras definiciones son: Decimos que tenemos una matriz diagonal si aij=0 para i≠j sin importar el valor que tomen los elementos de la diagonal principal de la matriz. Una vez que hemos definido el concepto de matriz diagonal, definiremos que es una matriz triangular superior e inferior, si tenemos una matriz cuadrada A decimos que tenemos una matriz A triangular superior si: aij=0 siempre y cuando i>j y decimos que A es una matriz triangular inferior si: aij=0 siempre y cuando i
aula.tareasplus.com/Roberto-Cuartas/ALGEBRA-LINEAL/Matrices-Triangulares
Matrices in Math; the Matrix and How it Works | SchoolTutoring.com
A matrix is a rectangular arrangement of “mn” elements with ‘m’ rows and ‘n’ columns enclosed within brackets.
www.schooltutoring.com/help/understanding-matrices-in-math/
Learn History of Matrices | Need Math Help
Learn History of Matrices Introduction:- The history of matrices goes back to ancient times, But the term “Matrix” was not applied to the concept until 1850.  “Matrix” is the Latin word for womb, and it retains that sense in English.
needmathhelp.wordpress.com/2013/04/05/learn-history-of-matrices/
r - Faster way of calculating off-diagonal averages in large matrices - Stack Overflow
stackoverflow.com/questions/13914845/faster-way-of-calculating-off-diagonal-averages-in-large-matrices
whats the physical significance of the off-diagonal element in the matrix of moment of inertia
In classical mechanics about rotation of rigid object, the general problem is to study the rotation on a given axis so we need to figure out the moment of inertia around some axes..
www.rqgg.net/topic/mpsru-whats-the-physical-significance-of-the-off-diagonal-element-in-the-matrix-of-moment-of-inertia.html
Interest Rate Modelling: Principal Component Analysis (PCA) : How to conduct a Principal Component Analysis in Excel: Diagonal Matrix | Finance Training Course
financetrainingcourse.com/education/2010/11/interest-rate-modelling-principal-component-analysis-pca-how-to-conduct-a-principal-component-analysis-in-excel-diagonal-matrix/
Iam Architect: House Playa El Golf H4
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