We introduce some new algebraic and topological properties of the Minkowski inverse A([Symbol: see text) of an arbitrary matrix A[Symbol: see text] M m,n (including singular and rectangular) in a Minkowski space μ. Furthermore, we show that the Minkowski inverse A ([Symbol: see text]) in a Minkowski space and the Moore-Penrose inverse A(+) in a Hilbert space are different in many properties suc...

The aim of this work is to prove the existence and uniqueness Drazin inverse DMP inverses a bounded finite potent endomorphism. In particular, we give main properties these generalized inverses, offer their relationships with adjoint operator, study spectrum, compute respective traces determinants relate operator classical definitions inverse. Moreover, different Moore-Penrose are studied.

The backpropagation algorithm, which had been originally introduced in the 1970s, is the workhorse of learning in neural networks. This backpropagation algorithm makes use of the famous machine learning algorithm known as Gradient Descent, which is a first-order iterative optimization algorithm for finding the minimum of a function. To find a local minimum of a function using gradient descent, ...

The extreme learning machine (ELM) that is proposed by Huang is designed based on single-hidden layer feedforward neural networks (SLFNs), which can randomly choose the parameters of hidden nodes and the output weights gotten analytically. So it can get the solution fastly. However, the learning time of ELM is mainly spent on calculating the Moore-Penrose generalized inverse matrices of the hid...

We present in this work the performances of a mobile omnidirectional robot through evaluating its management of the redundancy of actuation. Thus we come to the predictive control implemented. The distribution of the wringer on the robot actions, through the inverse pseudo of Moore-Penrose, corresponds to a « geometric ›› distribution of efforts. We will show that the load on vehicle wheels wou...

This paper establishes some perturbation analysis for the tensor inverse, Moore-Penrose and system based on t-product. In settings of structured perturbations, we generalize Sherman-Morrison-Woodbury (SMW) formula to t-product scenarios. The SMW can be used perform sensitivity a multilinear equations.

The recursive method for computing the generalized LM inverse of a constant rectangular matrix augmented by a column vector is proposed in [16, 17]. The corresponding algorithm for the sequential determination of the generalized LM -inverse is established in the present paper. We prove that the introduced algorithm for computing the generalized LM inverse and the algorithm for the computation o...

For a sample of n independent identically distributed p-dimensional centered random vectors with covariance matrix Σn let S̃n denote the usual sample covariance (centered by the mean) and Sn the non-centered sample covariance matrix (i.e. the matrix of second moment estimates), where p > n. In this paper, we provide the limiting spectral distribution and central limit theorem for linear spectral...

Extensions of the Schur complement and the principal pivot transform, where the usual inverses are replaced by the Moore-Penrose inverse, are revisited. These are called the pseudo Schur complement and the pseudo principal pivot transform, respectively. First, a generalization of the characterization of a block matrix to be an M -matrix is extended to the nonnegativity of the Moore-Penrose inve...

A complex square matrix A is said to be idempotent, or a projector, whenever A2 = A; when A is idempotent, and Hermitian (or real symmetric), it is often called an orthogonal projector, otherwise an oblique projector. Projectors are closely linked to generalized inverses of matrices. For example, for a given matrix A the product PA = AA + is well known as the orthogonal projector on the range (...