I
... It is a closed set (in both the Euclidean and Zariski sense) as it can be described algebraically: Seg(Rl , Rm , Rn ) = {A ∈ Rl×m×n | A = u ⊗ v ⊗ w} = {A ∈ Rl×m×n | ai1 i2 i3 aj1 j2 j3 = ak1 k2 k3 al1 l2 l3 , {iα , jα } = {kα , lα }} Hypermatrices that have rank > 1 are elements on the higher secant ...
... It is a closed set (in both the Euclidean and Zariski sense) as it can be described algebraically: Seg(Rl , Rm , Rn ) = {A ∈ Rl×m×n | A = u ⊗ v ⊗ w} = {A ∈ Rl×m×n | ai1 i2 i3 aj1 j2 j3 = ak1 k2 k3 al1 l2 l3 , {iα , jα } = {kα , lα }} Hypermatrices that have rank > 1 are elements on the higher secant ...
An Overview of Compressed sensing
... Whether a signal is “sparse” depends on the basis used. For example, a vector x denoting time samples of a signal may not be sparse, but its discrete cosine transform (or discrete Fourier transform) may be sparse. The use of the DFT requires measurement matrices with complex elements, but the theory ...
... Whether a signal is “sparse” depends on the basis used. For example, a vector x denoting time samples of a signal may not be sparse, but its discrete cosine transform (or discrete Fourier transform) may be sparse. The use of the DFT requires measurement matrices with complex elements, but the theory ...
Graph Parameters via Operator Systems
... only depend on a vector space of matrices associated with the quantum channel, i.e., two quantum channels that define the same vector space have the same capacity. They argued that the study of these spaces of matrices should be treated as a kind of non-commutative graph theory. This is the main ide ...
... only depend on a vector space of matrices associated with the quantum channel, i.e., two quantum channels that define the same vector space have the same capacity. They argued that the study of these spaces of matrices should be treated as a kind of non-commutative graph theory. This is the main ide ...
