Sentence examples for matrix with orthonormal from inspiring English sources

where W ∈ Rn×mis a matrix with orthonormal columns.

(tilde {mathbf {V}}^{n}_{ij}) is a full rank matrix with orthonormal columns.

For, there exists a matrix with orthonormal columns with size satisfying (D1).

where C c denotes the reduced DCT matrix with orthonormal rows.

Further, we let be a unitary matrix with orthonormal columns in the null space of such that.

A sketch of proof is given in Appendix E. We let be unitary matrix with orthonormal columns in the null space of such that.

(mathcal {U}(M_{t},M)) denotes the set of M t ×M matrices with orthonormal columns.

We consider the singular value decomposition (SVD) of a matrix A of rank r A=USV^{H},quad S=operatorname{diag}bigl({sigma_{i}}bigr), 1leq ileq r, where U and V are (mtimes r) and (ntimes r) matrices with orthonormal columns, respectively, and (sigma_{i}) is the positive singular values.

Since both (tilde {mathbf {V}}^{n}_{ij}) and Q n are matrices with orthonormal columns and (tilde {mathbf {V}}^{n}_{ij} = mathbf {Q}^{n}mathbf {V}^{n}_{ij}), the columns of (mathbf {V}^{n}_{ij} in mathbb {C}^{T times T_{sig}}) are also normalized and orthogonal with each other.

where is an orthonormal matrix with its columns constituting an orthonormal basis for the null space.

That is: Where T is an orthonormal matrix of dimensions m x m, S is a diagonal matrix of dimensions m x n and D is an orthonormal matrix with dimensions n x n.