Suppose that D is a division ring in which there is defined an anti-automorphism α→(?)is involutorial,R is a left vector space over D.Using the given anti-automorphism α→(?),it is easy to turn R into a right vecto...Suppose that D is a division ring in which there is defined an anti-automorphism α→(?)is involutorial,R is a left vector space over D.Using the given anti-automorphism α→(?),it is easy to turn R into a right vector space over D by seting x(?)=ax.Bilinear form g(x,y)connecting the left vector space R and the right vector space R is a Hermitian scalar.展开更多
Let A∈C<sup>m×n</sup>,set eigenvalues of matrix A with |λ<sub>1</sub> （A）|≥|λ<sub>2</sub>（A）|≥…≥|λ<sub>n</sub>（A）|,write A≥0 if A is a positive semid...Let A∈C<sup>m×n</sup>,set eigenvalues of matrix A with |λ<sub>1</sub> （A）|≥|λ<sub>2</sub>（A）|≥…≥|λ<sub>n</sub>（A）|,write A≥0 if A is a positive semidefinite Hermitian matrix, and denote∧<sub>k</sub> （A）=diag （λ<sub>1</sub>（A）,…,λ<sub>k</sub>（A））,∧<sub>(</sub>（n-k）.（A）=diag (λ<sub>k+1</sub>（A）,…,λ<sub>n</sub>（A）)for any k=1, 2,...,n if A≥0. Denote all n order unitary matrices by U<sup>n×n</sup>.Problem of equalities to hold in eigenvalue inequalities for products of matrices展开更多
We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
文摘Suppose that D is a division ring in which there is defined an anti-automorphism α→(?)is involutorial,R is a left vector space over D.Using the given anti-automorphism α→(?),it is easy to turn R into a right vector space over D by seting x(?)=ax.Bilinear form g(x,y)connecting the left vector space R and the right vector space R is a Hermitian scalar.
基金Supported partly by National Natural Science Foundation of China
文摘Let A∈C<sup>m×n</sup>,set eigenvalues of matrix A with |λ<sub>1</sub> （A）|≥|λ<sub>2</sub>（A）|≥…≥|λ<sub>n</sub>（A）|,write A≥0 if A is a positive semidefinite Hermitian matrix, and denote∧<sub>k</sub> （A）=diag （λ<sub>1</sub>（A）,…,λ<sub>k</sub>（A））,∧<sub>(</sub>（n-k）.（A）=diag (λ<sub>k+1</sub>（A）,…,λ<sub>n</sub>（A）)for any k=1, 2,...,n if A≥0. Denote all n order unitary matrices by U<sup>n×n</sup>.Problem of equalities to hold in eigenvalue inequalities for products of matrices
文摘We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
