In terms of power conservation, it is clear that our system can reduce much more tune-in time if a proper indexing technology is applied to our index channel.
Definition 1.2 The tensor A is called reducible if there exists a nonempty proper index subset J ⊂ { 1, 2, …, n } such that a i 1, i 2, …, i m = 0, ∀ i 1 ∈ J, ∀ i 2, …, i m ∉ J.
Definition 1.1 The tensor is called reducible if there exists a nonempty proper index subset J ⊂ { 1, 2, …, n } such that a i 1, i 2, …, i m = 0, ∀ i 1 ∈ J, ∀ i 2, …, i m ∉ J.
(mathcal{A}) is called reducible if there exists a nonempty proper index subset (mathbb{J}subset N) such that a_{i_{1}i_{2}cdots i_{m}}=0, quad forall i_{1}inmathbb{J}, forall i_{2},ldots,i_{m}notinmathbb{J}.
The tensor (mathcal{A}) is called reducible if there exists a nonempty proper index subset (mathbb{J}subset N) such that (a_{i_{1}i_{2}cdots i_{m}}=0), (forall i_{1}inmathbb{J}), (forall i_{2},ldots,i_{m}notinmathbb{J}).
Here a tensor (mathcal{A}=(a_{i_{1}cdots i_{m}}) in R^{m,n}) is called reducible, if there exists a nonempty proper index subset (Isubset N) such that a_{i_{1}i_{2}cdots i_{m} }=0 quad mbox{for all } i_{1}in I, mbox{for all } i_{2},ldots,i_{m}notin I.
A complex tensor (mathcal{A}=(a_{i_{1}cdots i_{m}})) of order m dimension n is called reducible, if there exists a nonempty proper index subset (Isubset N) such that a_{i_{1}i_{2}cdots i_{m} }=0, quad forall i_{1}in I, forall i_{2},ldots,i_{m}notin I.
A tensor (mathcal{A}=(a_{i_{1}cdots i_{m}})) of order m and dimension n is called reducible if there exists a nonempty proper index subset (alphasubset N) such that a_{i_{1}i_{2}cdots i_{m}}=0,quad forall i_{1}inalpha, forall i_{2},ldots,i_{m} notinalpha.
The tensor (mathcal {A}) is called reducible if there exists a nonempty proper index subset (mathbb{J} subset{ 1,2,ldots,n }) such that (a_{i_{1},ldots,i_{m},i_{m}} = 0), (forall i_{1} inmathbb{J}), (forall i_{2}, ldots, i_{m} notinmathbb{J}).
