Learn the orthogonal matrix definition and its properties. Also, learn how to identify the given matrix is an orthogonal matrix with solved examples at BYJU'S.
a numerical algorithm for constructing a random symplecticorthogonal matrixis put forward.───给出了一种构造完全随机的正交辛矩阵的数值实现方法。 Anorthogonal matrixis an invertible matrix for which the inverse is equal to the transpose.───正交矩阵是可逆矩阵,其逆矩阵等于其转置矩阵。
An orthogonal matrix is defined as a matrix whose inverse is equal to its transpose. It is characterized by having orthogonal columns of unit length, making it a key concept in linear algebra and matrix operations. AI generated definition based on: Numerical Linear Algebra with Applications, 2015...
a.Of or relating to a matrix whose transpose equals its inverse. b.Of or relating to a linear transformation that preserves the length of vectors. 3.Very different or unrelated; sharply divergent:"Radical Islamists are ultimately seeking to create something orthogonal to our model of democracy"...
Table 1 A collection of connection problems resulting from banded matrix factorizations Full size table 1.1 Previous Work Polynomial and rational measure modifications and its connection problem in Theorem 1.3 are classical problems discussed at length in Gautschi’s book on computational orthogonal polynomi...
Let A be an l×k,k<l, matrix with column vectors, ai,i=1,…,k, and x an l-dimensional vector. The orthogonal projection of x on the subspace spanned by the columns of A (assumed to be linearly independent) is given by (Appendix A) (5.65) where in complex spaces the transpose ...
) is a tensor of order two, i.e., A is a matrix. If b ∈ T (m 1 ), then A· b (2) = A T b in matrix notation. Similarly, if c ∈ T (m 2 ), then A· c (1) = Ac. Lemma 2.5. Let U ∈ D as defined in (2.1) and A ∈ T . Then A· U = A· u...
If A is a rotation matrix (i.e., unitary determinant, with transpose and inverse coincide), then applying a rotation to both vectors would apply the same rotation to their cross product: (Av)×(Au)=A(v×u). The shape of the cross matrix is in line with the ijk multiplication rule ...
where “H” denotes a conjugate transpose. The base station estimates the channel response matrix H(k,t) for each subband, e.g., based on pilots transmitted by the terminals. The base station then uses the estimated channel response matrix {circumflex over (H)}(k,t) to derive the spatial...
This equation is based on the fact that the product of a Hadamard matrix and its transpose is the identity matrix, i.e. the transpose of a Hadamard matrix is its inverse. The codeword received over the wires can thus be multiplied by the transpose of the Hadamard matrix used to perform ...