Conference PaperPDF Available

New operations of matrix products for application of radars

  • October 1997
DOI:10.1109/DIPED.1997.710918
  • Conference: Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, 1997. DIPED-97
Authors:
Vadym Slyusar at Central Scientific Research Insitute of Armaments and Military Equipment of Armed Forces of Ukraine
Vadym Slyusar
  • Central Scientific Research Insitute of Armaments and Military Equipment of Armed Forces of Ukraine
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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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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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Under consideration of multi coordinate digital antenna arrays (DAA) there is the problem of compact matrix record of the reception channels. The known mathematical apparatus does not allow to use habitually for the perception structures of matrixes, describing directivity characteristics of the antenna elements and amplitude-frequency characteristics of the filters. For the solution of the given problem, it is offered to operate with a special type of the product of matrixes, named by the author as "face-splitting".