We met the idea of a linear combination of matrices in chapter 3. We will now expand the definition so that we can talk about linear combinations of elements of any vector space. A sequence which is ...

This course is part of the Mathematics for Machine Learning and Data Science Specialization by DeepLearning.AI. After completing this course, learners will be able to: Represent data as vectors and ...

Abstract: Constructing linear combinations of idempotent matrices is one of important issues. This paper firstly proposes the definition of n - by - n idempotent matrix of k. Then, the conditions that ...

In the theory of vector spaces, a set of vectors is said to be linearly independent if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear ...

Abstract: Linear transforms are often used to adapt the acoustic models in speech recognition systems. When there is very little (5–10 sees.) acoustic data adaptation suffers from unreliable parameter ...

In this paper we analyze the Banach *-algebra of time-frequency shifts with absolutely summable coefficients. We prove a noncommutative version of the Wiener lemma. We also construct a faithful ...