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| Mathematics Department | Non mathematics Majors |
| Matrix order | Less than 4 | Any high order (up to hundreds) |
| Theory | Classical theory for small matrices | Theory adapt to large matrices |
| Tools and results | Pencil, symbolic formula | Computer, numerical & symbolic results |
| Emphasized on | Abstract thinking of N-dimension | 3-D spatial concept |
| Applications | Few examples of small integer matrices | Real world complex problems in many area |