Explicit formulas for the Jordan normal forms and matrix exponentials of 2 × 2 matrices

Key Points

• The aim is to derive explicit formulas for the Jordan normal forms and matrix exponentials of 2x2 matrices.
• Derived explicit formulas for Jordan normal forms.
• Provided formulas for matrix exponentials.
• Emphasized the use of basic arithmetic operations.
• Presented clear formulas that simplify understanding Jordan normal forms.
• Demonstrated explicit matrix exponential calculations.
• Showed the feasibility of the entire theory with basic operations.