This research presents clear formulas for Jordan normal forms and matrix exponentials in 2x2 matrices, suggesting a simplification of linear algebra concepts.
We present an explicit formula of the Jordan normal forms of 2 × 2 matrices and give explicit formulas of 2 × 2 matrix exponentials. While the general theory is abstract, we will demonstrate that the entire theory can be completed using only the four basic arithmetic operations in the case of 2 × 2 matrices.
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Hiroyuki Chihara (2026) studied this question.
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