A new approach to the concept of linearity. Some elements for a multiplicative linear algebra

ABSTRACT

An arithmetic based on the multiplication is the base of the Bigeometric (and Multiplicative) Calculus, a type of non-Newtonian Calculus which has had uses in the digital processing of images. In this work, we present the fundamental elements to construct a proposal of Multiplicative Linear Algebra with view of being a support for a Multiplicative Calculus in Several Variables and its applications. Some important concepts such as vector space, linear transformation and matrix representation are reviewed. In particular, we give a meaning and context to the operation: matrix raised to matrix.

KEYWORDS:

• Non-Newtonian calculus
• linearity
• matrices exponentiation
• multiplicative linear algebra
• multiplicative linear transformations

2010 AMS SUBJECT CLASSIFICATION:

• 15A99

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was founded by a grant of CONICYT. PAI-Academia 79150021.