Sentence examples for matrix vectorization operation from inspiring English sources

where vec denotes the matrix vectorization operation, R i = R Tx, i T ⊗ R Rx, i, and ⊗ denotes the Kronecker product.

A ⊗ B denotes the Kronecker product of A and B. vec and unvec are the matrix vectorization operator and the inverse matrix vectorization operator, respectively.

E and ℜ z) denote the expectation of a random variable and real part of z. vec gives matrix vectorization operator, and ⊗ represents the Kronecker operator.

To see that the 16 parameters of T conform to this special structure, consider the 16 dimensional parameter column-vector (19) T ˜ = ln { vec T }, where 'vec' is the standard matrix-vectorization operator.

The proposed method firstly performs the vectorization operation on the covariance matrix, which is calculated from the latest received data matrix obtained by a reduced dimensional transformation.

Then, we would introduce a basic property of vectorization operation that will be useful in the sequel.

We will use (mathbb {E} left [ cdot right ] ) for expectation, v e c for matrix vectorization, t r for the matrix trace, ⊗ for the Kronecker product, and I N for the N×N identity matrix.

Then, the measurement-signal relationship becomes (A.3) Y ≜ y 1, y 2, …, y T = F X Φ H. Using the property vec(A B C) = (A ⊗ C H vec BB), where vec denotes columnwise vectorization operation, we have (A.4) y = F ⊗ Φ x = A x, where y = vec(Y) ∈ ℂ mT and x = vec(X) ∈ ℂ nT.

Upper (lower) bold face letters will be used for matrices (vectors);,,,,, and denote conjugate, transpose, Hermitian transpose, mathematical expectation, identity matrix, and Frobenius norm, respectively.,,, denote the matrix trace operator, vectorization operator, space of matrices with complex entries, and the Kronecker product, respectively.

where denotes the matrix-vector transpose operation.

vec denotes the vectorization operator that turns a matrix into a vector by concatenating all the columns, and diag{x} denotes a diagonal matrix with the elements of x constituting the diagonal entries.