Sentence examples for matrix and tilde from inspiring English sources

where (tilde {boldsymbol {M}}_{h}) is a generalized mass matrix and (tilde {boldsymbol {h}}_{h}) is a generalized force vector.

where is the th row of the matrix and "tilde" is used to denote a vector concatenated with the scalar.

where (bar {boldsymbol {D}}_{s}) is an M×M deterministic matrix and (tilde {boldsymbol {D}}_{s}) is an M×M diagonal matrix with ([tilde {boldsymbol {D}}_{s}]_{mm} =beta ).

where (Lambda =text {diag}left ({lambda _{1}^{2}},ldots,{lambda _{N}^{2}}right)) and λ n denotes the singular values of Δ X . Vis a unitary matrix and (tilde {mathbf {h}}=mathbf {V} mathbf {h}).

Hence, by defining (tilde {mathbf {H}}_{c(i),k}= mathbf {Q}_{r}mathbf {H}_{c(i),k}) as the post-processed equivalent channel matrix and (tilde {mathbf {Z}}_{c(i),k}= mathbf {Q}_{r}mathbf {Z}_{c(i),k}) as the normalized interference plus noise, (2) is revised as tilde{mathbf{y}}_{k} = tilde{mathbf{H}}_{c(i),k}sum_{j=1}^{U_{c(i)}}mathbf{W}_{c(i),j}mathbf{s}_{c(i),j} + tilde{mathbf{Z}}_{c(i),k}. (3).

The vector-valued function (hat{g}_{i}(cdot)) is assumed to satisfy the following sector-bounded condition, namely for (forall x, yin mathbb{R}^{n}): bigl[hat{g}(x -hat{g}(y)-N_{1}(x -hat{g]^{T} y -N_{hat{g} y -N_{ {g}(y)-N_{2}(x-y)bigr]leq0, where (N_{1} x-y bigr) are known real constant matrices, and (tilde {N}=N_{1} x-y bigrs a symmetric positive definite matrix.

Similar as the energy arrival model, we express the state transition probability matrix between E t and (tilde {E}_{t}) as a policy matrix P with elements p i,j ∈{0,1},∀i,j denoting the event of using (i−j) unites of energy in state E t =i.

Define the diagonal matrix (tilde {D}) whose entries are column sums of the weight matrix (tilde {W}), and (tilde {L}=tilde {D}-tilde {W}) is a Laplacian matrix.

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 (mathbf {I}_{tilde {N}}) is a (tilde {N} times tilde {N}) identity matrix and Γ zi is a (N_{c} times tilde {N}) sparse matrix of ±1 elements linking the eliminated variables x zi to the remaining ones.

where (tilde {A}) is weighted adjacency matrix of directed networks, (tilde { D}_{O}) is the weighted diagonal matrix of out-degrees (or row sum of (tilde {A})) and (tilde {D}_{I}) is the weighted diagonal matrix of in-degrees (or column sum of (tilde {A})).