2 A denote the transpose, Moore-Penrose generalized inverse, Frobenius norm and Euclid norm, respectively. For any , m n A B  R ,   , 0 T A B trace B A   denotes the inner product of A and B . Therefore, m n R  is a complete inner product space endowed with 2 , A A A  . For any non-zero matrices 1 2 , , , m n k A A A  R  , if  , T j i i A A trace A     0 j A i j   , then it is...

A novel training algorithm for nonlinear discriminants for classification and regression in Reproducing Kernel Hilbert Spaces (RKHSs) is presented. It is shown how the overdetermined linear leastsquares-problem in the corresponding RKHS may be solved within a greedy forward selection scheme by updating the pseudoinverse in an order-recursive way. The described construction of the pseudoinverse ...

A denotational semantics of quantum Turing machines having a quantum control is defined in the dagger compact closed category of finite dimensional Hilbert spaces. Using the Moore-Penrose generalized inverse, a new additive trace is introduced on the restriction of this category to isometries, which trace is carried over to directed quantum Turing machines as monoidal automata. The JoyalStreet-...

-.m. , A program is described which computes the pseudoinverse, and oth:'3r related quantities, of an m X n matrix A of unknown rank. The program obtains least square solutions to singular and/or inconsistent linear systems Ax = B, where m 5 n or m > n and the rank of A ma.y be less than min(m,n). A complete description of the program and its use is given, including computational experience on ...

In a string x on an alphabet Σ, a position i is said to be indeterminate iff x[i] may be any one of a specified subset {λ1, λ2, . . . , λj} of Σ, 2 ≤ j ≤ |Σ|. A string x containing indeterminate positions is therefore also said to be indeterminate. Indeterminate strings can arise in DNA and amino acid sequences as well as in cryptological applications and the analysis of musical texts. In this ...