Abstract
Linear algebra is introduced using simultaneous equations. Linear transformations are used to introduce the idea of vectors and matrices. The concept of a finite dimensional linear vector space is introduced for describing the properties of vectors. Basis vectors and rules for vector addition and scalar products are defined. Linear transformation are interpreted as the action of matrices on vectors and which yields the defining equations of how vectors are transformed under the action of matrices. The generalization of vectors to N-dimensions is made.
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Notes
- 1.
In curved spaces, one cannot move around vectors and the concept of parallel transport is required, which depends on the path taken for moving a vector from one point to another. The change of the vector undergoing parallel transport depends on the curvature of the space.
- 2.
The tensor product of two vectors is discussed later.
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Baaquie, B.E. (2020). Simultaneous Linear Equations. In: Mathematical Methods and Quantum Mathematics for Economics and Finance. Springer, Singapore. https://doi.org/10.1007/978-981-15-6611-0_2
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DOI: https://doi.org/10.1007/978-981-15-6611-0_2
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Online ISBN: 978-981-15-6611-0
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