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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. In the remainder of this article we will consider only square diagonal matrices, and refer to them ...
The entries form the main diagonal of a square matrix. For instance, the main diagonal of the 4×4 matrix above contains the elements a 11 = 9, a 22 = 11, a 33 = 4, a 44 = 10. In mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order .
A square and a crossed square have the following properties in common: Opposite sides are equal in length. The two diagonals are equal in length. It has two lines of reflectional symmetry and rotational symmetry of order 2 (through 180°). It exists in the vertex figure of a uniform star polyhedra, the tetrahemihexahedron.
In mathematics, a square matrix is said to be diagonally dominant if, for every row of the matrix, the magnitude of the diagonal entry in a row is greater than or equal to the sum of the magnitudes of all the other (off-diagonal) entries in that row.
According to the characterization of these quadrilaterals, the two red squares on two opposite sides of the quadrilateral have the same total area as the two blue squares on the other pair of opposite sides. In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles.
A square matrix with entries 0, 1 and −1 such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. Anti-diagonal matrix: A square matrix with all entries off the anti-diagonal equal to zero. Anti-Hermitian matrix: Synonym for skew-Hermitian matrix. Anti-symmetric matrix
An square matrix with entries in a field is called diagonalizable or nondefective if there exists an invertible matrix (i.e. an element of the general linear group GL n (F)), , such that is a diagonal matrix.
A pan-diagonal magic square remains a pan-diagonal magic square under cyclic shifting of rows or of columns or both. [69] This allows us to position a given number in any one of the n 2 cells of an n order square. Thus, for a given pan-magic square, there are n 2 equivalent pan-magic squares. In the example below, the original square on the ...