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	Main diagonal
		In linear algebra, the main diagonal of a square matrix is the diagonal which runs from the top left corner to the bottom right corner.
		A matrix like the above in which only the elements of the main diagonal are non-zero is called a diagonal matrix.
		The sum of the entries on the main diagonal of a matrix is known as the trace of that matrix.
	www.ebroadcast.com.au /lookup/encyclopedia/ma/Main_diagonal.html (92 words)

	Diagonal - Wikipedia, the free encyclopedia
		In engineering a diagonal brace is a beam used to cross brace a rectangular structure such as scaffolding to withstand sheer forces pusing into a rhombus; although called diagonal, due to practical considerations in practice diagonal braces are often not connected to the corners of the rectangle.
		Diagonal pliers are wire-cutting pliers defined by the cutting edges of the jaws intersects the joint rivet at an angle or "on a diagonal", hence the name.
		In general, the intersection number of the graph of a function with the diagonal may be computed using homology via the Lefschetz fixed point theorem; the self-intersection of the diagonal is the special case of the identity function.
	en.wikipedia.org /wiki/Diagonal (816 words)

	[No title]
		Notice that both the left and right main diagonals of the table in Illustration 1.1 have the Euler property, however none of the rows or columns have the Euler property, since the Euler items in each row all have the same color and the Euler items in each column all have the same shape.
		Start with the left main diagonal having the green circle at the top left and the blue triangle in the second position below the green circle on this diagonal.
		Start with the left main diagonal having the green circle at the top left and the blue triangle in the third position below the green circle on this diagonal.
	www.mi.sanu.ac.yu /vismath/pais/pais1/pais1.html (1372 words)

	Equations
		The pivot is the element of the main diagonal that is on the current row.
		Since the zeros below the main diagonal did not change, you now have a diagonal matrix to the left of the bar because all the non-zero elements lie on the main diagonal.
		Since all the elements along the diagonal of this diagonal matrix are the number one, this matrix is the identity matrix.
	ceee.rice.edu /Books/LA/equations/index.html (1977 words)

	MAT 200 Lecture Notes -- Lemmas About Matrices
		The diagonal line from the upper left hand corner of a square matrix to the lower right hand corner is called the main diagonal.
		We have already seen the main diagonal once before, in the definition of identity matrices; the non-zero entries were the ones on the main diagonal.
		The sum of the entries on the main diagonal of a square matrix A is called the trace of A and is denoted tr(A).
	www.math.princeton.edu /~stalker/200f99/notes_4.html (584 words)

	Main Daigonals and Euler's Totient (Site not responding. Last check: 2007-11-03)
		The diagonal enters a new little cube each time it passes through a "wall", and (starting from the negative region) we know it passes through 150 walls in the x direction, 324 in the y direction, and 375 in the z direction, for a total of 849.
		However, some of these transitions from one cell to another occur when the diagonal line passes through more than one wall at once.
		For example, the diagonal enters the very first cell at one of its vertices (the 0,0,0 point), so it's passing through 3 walls but entering only one new region.
	www.mathpages.com /home/kmath328.htm (248 words)

	[No title]
		So, the new right main diagonal starting from the upper right and proceeding down and to the left should be: the large yellow square with thin border, the small yellow square with fat border, the large green triangle with thin border, and the small green triangle with fat border.
		Note that one similarity class {0, 5, 10, 15, 3, 6, 9, 12} occurs on the two main diagonals, and the other similarity class {14, 13, 2, 1, 11, 7, 8, 4} occurs in the middle of the top and bottom rows, and in the middle of the leftmost and rightmost columns of the table.
		Next, since we must have the same similarity class occupying the left main diagonal, we have 6 choices remaining for the first position below a on this diagonal, say b, and then b' must go below a' in the last position on this diagonal.
	www.mi.sanu.ac.yu /vismath/pais/pais2/pais2.html (4453 words)

	Tri-Diagonal Linear Systems
		The idea that is often used is to call elements of the main diagonal
		Create a 31 by 31 tridiagonal matrix A where the main diagonal elements are all "2" and all elements of the subdiagonal and superdiagonal elements are "1." Then solve the linear system
		Since the matrix is tri-diagonal and diagonally dominant, there are other algorithms which can be used to compute the solution.
	math.fullerton.edu /mathews/n2003/Tri-DiagonalMod.html (483 words)

	The Shape of Coincidence (Site not responding. Last check: 2007-11-03)
		Disregarding the "clipping" at the boundaries, this "region of coincidence" (within +-d of the diagonal) is simply the region swept out by a line segment of length dsqrt(2) normal to the main* diagonal.
		The region of coincidences is swept out by a regular hexagon normal to the main diagonal, so the "shape" of a three-event coincidence is a hexagon, with edge length d*sqrt(2/3).
		Since the solid is in the (n-1)-dimensional "plane" normal to the diagonal, the coordinates of the solid when it is located at the origin satisfy x1 + x2 +...
	www.mathpages.com /home/kmath276.htm (607 words)

	MAT 200 Lecture Notes -- Demand Laws
		The pattern on the main diagonal is that the entry in the i'th row, i'th column of a is the coefficient of the square of the i'th variable in the quadratic polynomial s.
		are all zero, the remaining entries on the main diagonal of a are all zero.
		The pattern off the main diagonal is that the entry in the i'th row j'th column of a is a half of the coefficient of the i'th variable time the j'th variable in the quadratic polynomial s.
	www.math.princeton.edu /~stalker/200s00/demand.html (1542 words)

	Matrix Market: Glossary
		A matrix is diagonally dominant if the absolute value of each diagonal element is greater than the sum of the absolute values of the other elements in its row (or column).
		A Hessenberg matrix is `almost' triangular, that is, it is (upper or lower) triangular with one additional off-diagonal band (immediately adjacent to the main diagonal).
		The Jordan normal form of a matrix is a block diagonal form where the blocks are Jordan blocks.
	math.nist.gov /MatrixMarket/glossary.html (756 words)

	Parahexes
		If the 3 main diagonals of a hexagon are concurrent, and the point of concurrence is the midpoint of each diagonal, then the hexagon is a parahexus.
		A corollary is that the diagonals of a parahexes are concurrent.
		In all cases, you can prove congruent triangles are formed by the sides and the main diagonals and that the main diagonals both bisect each other and are concurrent.
	staff.imsa.edu /math/journal/volume4/webver/parahex.html (852 words)

	Blind Source Separation
		Therefore, when the elements of the diagonal matrix are properly selected, it is possible to make the main diagonal elements of the output matrix equal to one.
		Without the removal of the main diagonal elements of G(z) there are an infinite number of solutions, one of which corresponds to the exact solution, even though all of them satisfy the convergent condition that the outputs are mutually independent.
		As previously stated, in a symmetric adaptive decorrelation architecture, the main diagonal elements of the demixing matrix, G(z), are removed and both N and M are equal to two.
	www.cnel.ufl.edu /info/bss.html (3935 words)

	Lecture 15 Recursion and Backtracking
		In order to make sure that two queens do not occupy the same column or the same diagonal, it is not necessary to save the complete 8 x 8 board.
		The main downward diagonal is identified by the positions (0,0), (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) and (7,7).
		The main upward diagonal is identified by the positions (0, 7), (1,6), (2, 5), (3, 4), (4,3), (5,2), (6,1) and (7,0).
	www.louisville.edu /~ecrouc01/CECS302/Lecture15.htm (954 words)

	Similarity Matrix and Beat Spectrum FAQ
		The similarity matrix for this signal will look like diagonal stripes, which are spaced at 1 second (in both dimensions) from the main diagonal.
		This is B(0), and should be a large number, as values on the main diagonal are maximum.
		So the beat spectrum is a function of time B(t), along the axis that we chose, whose values are the sums along diagonal lines a distance t from the main diagonal.
	www.fxpal.com /?p=similaritymatrixFAQ (1414 words)

	Matrix Market: Help With Matrix Statistics
		The number of diagonal bands required to represent the lower triangle of A in band storage mode is l, while the number of diagonal bands required to represent the upper triangle in band storage mode is u.
		The diagonal is indicated by its offset from the main diagonal; thus 0 is the main diagonal, -1 is the first lower diagonal and 2 is the second upper diagonal.
		For each of these diagonals we list the number of nonzeros, and the accumulated percent of matrix nonzeros found on this diagonal and all heavier ones.
	math.nist.gov /MatrixMarket/statHelp.html (696 words)

	Special Matrices: Triangular, Symmetric, Diagonal
		Its diagonal is given by the numbers a and d.
		Indeed, the diagonal subdivides the matrix into two blocks: one above the diagonal and the other one below it.
		A diagonal matrix is a symmetric matrix with all of its entries equal to zero except may be the ones on the diagonal.
	www.sosmath.com /matrix/matrix3/matrix3.html (345 words)

	Iso-like Magic Stars
		This is caused because the corner numbers in the square must appear in 4 different lines; the row, the column, the diagonal and a pan-diagonal.
		Because the 36 and the 16 also appear in the main diagonal, the two diagonals cannot be included without requiring duplicate numbers.
		This results in the main diagonals now also being correct, but at the cost of a loss in symmetry.
	www.geocities.com /~harveyh/panmagic.htm (2251 words)

	Block Diagonal Matrix (Site not responding. Last check: 2007-11-03)
		A block diagonal matrix has blocks along the main diagonal, and zeros elsewhere.
		You may have noticed that every matrix is block diagonal, consisting of one block running from 1 to n.
		Similarly, the trace of the matrix is the sum of the traces of the individual blocks.
	www.mathreference.com /la-jf,bdiag.html (515 words)

	Matrix Algebra (Site not responding. Last check: 2007-11-03)
		(The main or principal diagonal in matrix B is composed of elements all equal to 1.) With a square, symmetric matrix, the transpose of the matrix is the original matrix.
		A diagonal matrix is a square, symmetric matrix that has zeros everywhere except on the main diagonal.
		In it, we have variances on the diagonal and covariances off the main diagonal.
	luna.cas.usf.edu /~mbrannic/files/regression/matalg.html (1775 words)

	More Magic Squares
		All rows, columns, and the 2 main diagonals = 425.
		It is pan-diagonal so 4 rows, 4 columns, 2 main diagonals, 6 complementary diagonal pairs and 16 2 x 2 squares all sum to 19998.
		This square is composed of the consecutive series of numbers from 1 to 81 and as is usual with pure magic squares, all rows, columns, and the two main diagonals sum to the constant 369.
	www.geocities.com /~harveyh/moremsqrs.htm (1287 words)

	Extract Triangular Matrix (DSP Blockset)
		Upper -- Copies the elements on and above the main diagonal of the input matrix to an output matrix of the same size.
		The elements below the main diagonal of the output matrix are zero.
		The elements above the main diagonal of the output matrix are zero.
	www.weizmann.ac.il /matlab/toolbox/dspblks/extracttriangularmatrix.html (251 words)

	The Rook Problem
		place where the main diagonal intersects both a vertical and a horizontal line.
		When I cross the main diagonal I will have no upward moves remaining and one rightward move remaining.
		If, in a binary number that fits our criteria, I have ones stand for moves to the right and zeros stand for moves upward, the rook will never cross the main diagonal until the final zero and the rook will go from the lower left-hand corner to the upper right-hand corner.
	www.saintanns.k12.ny.us /depart/math/Seth/rook.html (1919 words)

	ZBL: Bottom Left (Clear Above Main Diagonal)
		The input matrix is read row by row, and all entries above the main diagonal are replaced by zero.
		All entries on or below the main diagonal remain unchanged, and the resulting matrix, row by row, is written out.
		Since the representation is in standard basis (so all the basis vectors are images of the first under the group) the diagonal entries of any fixed quadratic form must all be equal, so try each field entry in turn by adding that scalar matrix to the bottom half of the symplectic form.
	www.math.rwth-aachen.de /homes/Meataxe/htmldoc/node25.html (374 words)

	Gap version 4 - Compar-Introduction
		Lines parallel to the main diagonal represent contigs that are in the correct relative orientation to one another.
		Those perpendicular to the main diagonal show results for which one contig would need to be reversed before the pair could be joined.
		In the middle of the bottom right quadrant there is a blue diagonal line perpendicular to the main diagonal which indicates a pair of contigs that are in the wrong relative orientation.
	www.genome.ou.edu /staden/gap4_46.html (523 words)

	Finite Groups and Cayley Tables
		The fact that multiplication of numbers is commutative is readily visible by noting that the multiplication table is symmetrical about the main diagonal--the diagonal with the squares on it, 0, 1, 4, 9.
		The main diagonal is the one from the upper left corner to the lower right corner.
		Again by noticing the symmetry about the main diagonal we can see that this is an abelian group.
	members.tripod.com /~dogschool/cayley.html (1289 words)

	Eileen's Origami Page - Beginner's Guide to Crease Patterns
		Further point locations based on the kite fold are also possible, for example, the intersection between a diagonal a line drawn from one vertex of the kite fold to the corner of the square (Figure 1, right).
		The diagonal squares arrangement described above can also be thought of in terms of two strip grafts on adjacent edges of the square.
		Figure 3 (left) is an example of two strip grafts on either side of a main diagonal.
	spinflipper.com /origami/cp/tech2.html (792 words)

	6.4 - The Determinant of a Square Matrix
		A matrix in which all the non-zero elements are either on or above the main diagonal.
		A matrix in which all the non-zero elements are on the main diagonal.
		Once it's in triangular form, then all you have to do is multiply by the elements on the main diagonal and you have the determinant.
	www.richland.edu /james/lecture/m116/matrices/determinant.html (2597 words)

	The -factorization of Hessenberg-like plus diagonal matrices
		Givens transformations, transform the diagonal part into a Hessenberg matrix.
		When applying this technique to a semiseparable plus diagonal matrix, more general theorems concerning the structure, e.g., the structure of
		Moreover this will be used to solve systems of equations with the coefficient matrix of semiseparable plus diagonal form.
	www.cs.kuleuven.ac.be /~raf/homepage/publications/phd/node79.html (289 words)

	Matrix Manual: Matrix Decompositions
		B is upper bidiagonal and its main diagonal consists of the eigenvalues of A repeated according to their algebraic multiplicities.
		The matrix B is diagonal iff A is non-defective, i.e.
		The diagonal elements of D are the singular values of A.
	www.psi.toronto.edu /matrix/decomp.html (694 words)

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