Computation of Matrix Determinants by Cross-Multiplication: A Rethinking of Dodgson’s Condensation and Reduction by Elementary Row Operations Methods
We formulate a more straightforward, symmetry-based technique for manually computing the determinant of any <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>×</mo><m...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-07-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/7/1456 |
| Summary: | We formulate a more straightforward, symmetry-based technique for manually computing the determinant of any <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></semantics></math></inline-formula> matrix by revisiting Dodgson’s condensation method, as well as strategically applying elementary row (column) operations and the definition and properties of determinants. The result yields a more streamlined algorithm that is generalized through formulas and employs a smaller number of operations and succeeding matrices than the existing methods. |
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| ISSN: | 2073-8994 |