We extend Vandermonde matrices to generalized Vandermonde tensors. We call an ruth order n-dimensional real tensor A = （Ai1i2…im） a type-1 generalized Vandermonde （GV） tensor, or GV1 tensor, if there exists a vec...We extend Vandermonde matrices to generalized Vandermonde tensors. We call an ruth order n-dimensional real tensor A = （Ai1i2…im） a type-1 generalized Vandermonde （GV） tensor, or GV1 tensor, if there exists a vector v = （v1, v2,.. , Vn）T such that Aili2...im = vi2＋i3＋＋im-m＋l and call A , a type-2 （ruth order n dimensional） GV tensor, or GV2 tensor, if there exists an （m - 1）th order tensor B= （Bi1i2…im-1） such that Ai1i2…im= Bim-1i1i2…im In this paper, we mainly investigate the type-1 GV tensors including their products, their spectra, and their positivities. Applications of GV tensors are also introduced.展开更多
文摘We extend Vandermonde matrices to generalized Vandermonde tensors. We call an ruth order n-dimensional real tensor A = （Ai1i2…im） a type-1 generalized Vandermonde （GV） tensor, or GV1 tensor, if there exists a vector v = （v1, v2,.. , Vn）T such that Aili2...im = vi2＋i3＋＋im-m＋l and call A , a type-2 （ruth order n dimensional） GV tensor, or GV2 tensor, if there exists an （m - 1）th order tensor B= （Bi1i2…im-1） such that Ai1i2…im= Bim-1i1i2…im In this paper, we mainly investigate the type-1 GV tensors including their products, their spectra, and their positivities. Applications of GV tensors are also introduced.
