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TRACE AND NORM
"... Let L/K be a finite extension of fields, with n = [L: K]. We will associate to this extension two important functions L → K, called the trace and the norm. For each α ∈ L, let mα: L → L be multiplication by α: mα(x) = αx for x ∈ L. Each mα is a Klinear map from L to L, so choosing a Kbasis of L l ..."
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Let L/K be a finite extension of fields, with n = [L: K]. We will associate to this extension two important functions L → K, called the trace and the norm. For each α ∈ L, let mα: L → L be multiplication by α: mα(x) = αx for x ∈ L. Each mα is a Klinear map from L to L, so choosing a Kbasis of L
THE NORM AND TRACE
"... Abstract. The norm and trace can be defined for any finite field extension. In this paper, we shall be concerned with the properties of these two maps. We shall also discuss some applications in the special case when the extension is cyclic. It is presumed that the reader is reasonably familiar with ..."
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Abstract. The norm and trace can be defined for any finite field extension. In this paper, we shall be concerned with the properties of these two maps. We shall also discuss some applications in the special case when the extension is cyclic. It is presumed that the reader is reasonably familiar
Network Centric Warfare: Developing and Leveraging Information Superiority
 Command and Control Research Program (CCRP), US DoD
, 2000
"... the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technolo ..."
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Cited by 308 (5 self)
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the mission of improving DoD’s understanding of the national security implications of the Information Age. Focusing upon improving both the state of the art and the state of the practice of command and control, the CCRP helps DoD take full advantage of the opportunities afforded by emerging technologies. The CCRP pursues a broad program of research and analysis in information superiority, information operations, command and control theory, and associated operational concepts that enable us to leverage shared awareness to improve the effectiveness and efficiency of assigned missions. An important aspect of the CCRP program is its ability to serve as a bridge between the operational, technical, analytical, and educational communities. The CCRP provides leadership for the command and control research community by: n n
TRACE AND NORM, II
"... Let L/K be a finite Galois extension, with Galois group G = Gal(L/K). We can express characteristic polynomials, traces, and norms for the extension L/K in terms of G. Theorem 1.1. When L/K is a finite Galois extension with Galois group G and α ∈ L, χα,L/K(X) = ∏ (X − σ(α)). In particular, TrL/K(α) ..."
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Let L/K be a finite Galois extension, with Galois group G = Gal(L/K). We can express characteristic polynomials, traces, and norms for the extension L/K in terms of G. Theorem 1.1. When L/K is a finite Galois extension with Galois group G and α ∈ L, χα,L/K(X) = ∏ (X − σ(α)). In particular, Tr
Text Modeling with the Trace Norm
, 2006
"... We have two goals: (1) to find a lowdimensional representation of text that ..."
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We have two goals: (1) to find a lowdimensional representation of text that
TRACE
"... Let G be a finite group and let k be a field of char(k) = 2. We explicitly describe the set of trace forms of GGalois algebras over k when the virtual 2cohomological dimension vcd2(k) of k is at most 1. For fields with vcd2(k) ≤ 2 we give a cohomological criterion for the orthogonal sum of a tra ..."
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Let G be a finite group and let k be a field of char(k) = 2. We explicitly describe the set of trace forms of GGalois algebras over k when the virtual 2cohomological dimension vcd2(k) of k is at most 1. For fields with vcd2(k) ≤ 2 we give a cohomological criterion for the orthogonal sum of a
Results 1  10
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176,143