Abstract
Matrices are analyzed from first principles. The rules of matrix addition and multiplication are shown to follow from the definition of the transformation of a vectors by a matrix. The properties of 2\(\times \)2 matrices are used as an exemplars for the general features of matrices. The properties of determinants are discussed, and an explanation based on geometry is given for the significance of a determinant being zero. Central ideas of tenor (outer) product, eigenvalues and eigenvectors are discussed. A derivation is given of the spectral decomposition, using 2\(\times \)2 matrices as an example.
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Notes
- 1.
Recall for complex and real numbers, the expression 1/0 is undefined.
- 2.
Where the symbol \(\otimes \) is sometimes dropped if the expression has no ambiguity.
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© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
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Baaquie, B.E. (2020). Matrices. In: Mathematical Methods and Quantum Mathematics for Economics and Finance. Springer, Singapore. https://doi.org/10.1007/978-981-15-6611-0_3
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DOI: https://doi.org/10.1007/978-981-15-6611-0_3
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