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The diagonals of a cube with side length 1. AC' (shown in blue) is a space diagonal with length , while AC (shown in red) is a face diagonal and has length .. In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.
A square diagonal matrix is a symmetric matrix, so this can also be called a symmetric diagonal matrix. The following matrix is square diagonal matrix: [] If the entries are real numbers or complex numbers, then it is a normal matrix as well.
Any strictly diagonally dominant matrix is trivially a weakly chained diagonally dominant matrix. Weakly chained diagonally dominant matrices are non-singular and include the family of irreducibly diagonally dominant matrices. These are irreducible matrices that are weakly diagonally dominant, but strictly diagonally dominant in at least one row.
A magic square is an arrangement of numbers in a square grid so that the sum of the numbers along every row, column, and diagonal is the same. Similarly, one may define a magic cube to be an arrangement of numbers in a cubical grid so that the sum of the numbers on the four space diagonals must be the same as the sum of the numbers in each row, each column, and each pillar.
The trace of a matrix is the sum of the diagonal elements. The top-right to bottom-left diagonal is sometimes described as the minor diagonal or antidiagonal. The off-diagonal entries are those not on the main diagonal. A diagonal matrix is one whose off-diagonal entries are all zero. [4] [5]
(In the case of a lens with distortion, e.g., a fisheye lens, a longer lens with distortion can have a wider angle of view than a shorter lens with low distortion) [3] Angle of view may be measured horizontally (from the left to right edge of the frame), vertically (from the top to bottom of the frame), or diagonally (from one corner of the ...
Flat panel displays by contrast use the actual diagonal of their visible display size, thus the size is the actual size presented to the viewer in all markets. This means that a similarly specified size of display will be larger as a flat panel display compared with a cathode ray tube display.
The determinant of a diagonal matrix is simply the product of all diagonal entries. Such computations generalize easily to A = P D P − 1 {\displaystyle A=PDP^{-1}} . The geometric transformation represented by a diagonalizable matrix is an inhomogeneous dilation (or anisotropic scaling ).