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Results tagged with cauchy-schwarz-inequality
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user 22277
The Cauchy-Schwarz inequality states $|\langle x,y \rangle |\leq ||x||\cdot ||y||.$ Use this tag for questions related to the CS inequality and its applications.
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Are these $L_2$-spectral radii approximations strictly increasing?
Suppose that $V$ is a finite dimensional complex Hilbert space. Let $L(V)$ denote the collection of all linear mappings from $V$ to $V$. Let $A_1,\dots,A_r:V\rightarrow V$ be linear operators. Then de …
2
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When does the Cauchy-Schwarz inequality for spectral radii of tensor products become equality?
Let $V$ be a complex finite dimensional inner product space. If $A_{1},\dots,A_{n}:V\rightarrow V$ are linear operators, then let $\Phi(A_{1},\dots,A_{n}):L(V)\rightarrow L(V)$ be the superoperator de …
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Fractional reverse direction Cauchy-Schwarz inequality
If $Z_1,\dots,Z_r$ are complex $m\times m$-matrices, then let $\Phi(A_1,\dots,A_r):M_m(\mathbb{C})\rightarrow M_m(\mathbb{C})$ be the linear mapping defined by $\Phi(A_1,\dots,A_r)(X)=A_1XA_1^*+\dots+ …