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Application of Mathematical Models in Linear Algebra to the Metaverse Ecosystem

Application of Mathematical Models in Linear Algebra to the Metaverse Ecosystem

Özen Özer (Kırklareli University, Turkey), Biswadip Basu Mallik (Institute of Engineering and Management, Kolkata, India), and Gunjan Mukherjee (Brainware University, India)
Copyright: © 2023 |Pages: 24
DOI: 10.4018/978-1-6684-8851-5.ch013
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Abstract

Linear algebra is a branch of mathematics that is widely used throughout science and engineering. Linear algebra includes arithmetic operations with notation sharing. We can be able to have a better understanding of machine learning algorithms only after having a good understanding of linear algebra. Sometimes, machine learning might be pure linear algebra, involving many matrix operations; a dataset itself is often represented as a matrix. Linear algebra is used in data pre-processing, data transformations, and model evaluation. In this chapter, the basic importance of linear algebra has been discussed, and the close liaison of the subject with current research domain in machine learning and data science has been explored in the light of application of the same in solving some critical issues.
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Scalars, Vectors, Matrices And Tensors

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    A scalar is a single number which may appear inside any vector also. On the other hand, any vector consists of the scalar terms. The rules for scalar terms manipulation is different from the vector operation.

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    A vector is an array of numbers. A vector is represented as the collections of number of scalars. Any vector can be expressed as either the row matrix or column matrix. The operation on vectors follows specialized rules for vector operations.

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    A matrix is a 2-D array. It is the combination of number of vectors placed together one after another. The operation concerned are being performed on the 2D array following the rules of matrix.

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    Tensor defines the n dimensional data which can be represented as the grid of numbers or called as the N way array.

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