Conference PaperPDF Available

New operations of matrix products for application of radars

Authors:
  • Central Scientific Research Insitute of Armaments and Military Equipment of Armed Forces of Ukraine

Abstract

The new concept of face-splitting and transposed face-splitting matrix products is determined; its main characteristics and modifications of the new types of products for module matrices are considered
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matrixs
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pp
108
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May
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NEW OPERATIONS
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74
... We define the following notation of matrix products: · the regular matrix/vector/scalar product (if obvious from context, we neglect this symbol) F m×n × F n×n ′ → F m×n ′ ⋆ the star-product / Hadamard product F m×n × F m×n → F m×n ⊗ the Kronecker product F m×n × F m ′ ×n ′ → F mm ′ ×nn ′ ⊙ the column-wise Khatri-Rao product [29] F m×n × F m ′ ×n → F mm ′ ×n * the row-wise Khatri-Rao product / face-splitting product [29], [32] F m×n × F m×n ′ → F m×nn ′ It is easy to check (see, e.g., [32] and [33,Lemma 4.2.10.]) that for matrices A, B, C, D and a row vector z it holds that ...
... We define the following notation of matrix products: · the regular matrix/vector/scalar product (if obvious from context, we neglect this symbol) F m×n × F n×n ′ → F m×n ′ ⋆ the star-product / Hadamard product F m×n × F m×n → F m×n ⊗ the Kronecker product F m×n × F m ′ ×n ′ → F mm ′ ×nn ′ ⊙ the column-wise Khatri-Rao product [29] F m×n × F m ′ ×n → F mm ′ ×n * the row-wise Khatri-Rao product / face-splitting product [29], [32] F m×n × F m×n ′ → F m×nn ′ It is easy to check (see, e.g., [32] and [33,Lemma 4.2.10.]) that for matrices A, B, C, D and a row vector z it holds that ...
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