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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 matrix is a matrix with the same number of rows and columns. [5] An n-by-n matrix is known as a square matrix of order n. Any two square matrices of the same order can be added and multiplied. The entries a ii form the main diagonal of a square matrix. They lie on the imaginary line that runs from the top left corner to the bottom ...
A square matrix derived by applying an elementary row operation to the identity matrix. Equivalent matrix: A matrix that can be derived from another matrix through a sequence of elementary row or column operations. Frobenius matrix: A square matrix in the form of an identity matrix but with arbitrary entries in one column below the main diagonal.
Symmetry pattern of a bisymmetric 5 × 5 matrix. In mathematics, a bisymmetric matrix is a square matrix that is symmetric about both of its main diagonals. More precisely, an n × n matrix A is bisymmetric if it satisfies both A = A T (it is its own transpose), and AJ = JA, where J is the n × n exchange matrix. For example, any matrix of the form
The basic Weyr matrix in the top-left corner has the structure (4,2,1) and the other one has the structure (2,2,1,1). In mathematics, in linear algebra, a Weyr canonical form (or, Weyr form or Weyr matrix) is a square matrix which (in some sense) induces "nice" properties with matrices it commutes with. It also has a particularly simple ...
The linear complementarity problem (,) has a unique solution for every vector q if and only if M is a P-matrix. [4] This implies that if M is a P-matrix, then M is a Q-matrix. If the Jacobian of a function is a P-matrix, then the function is injective on any rectangular region of . [5]
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Download as PDF; Printable version ... In mathematics, a Q-matrix is a square matrix whose associated ... problem and spanning properties of complementary cones" (PDF).
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