[FEATURE] Add relevant information for any given matrix.

[CupapiOT]

Is your feature request related to a problem? Please describe.

It'd be quite helpful if there was information about the traits of a matrix. Right now, the matrices are just shown as they are--which is completely fine. Knowing any traits shouldn't hurt, though.

Describe the solution you'd like

A. Essential pieces of information for "useful calculator" necessities:

1. Determinant, trace, and rank
2. Eigenvalues + Eigenvectors
3. Inverse matrix

B. Secondary "nice to have" information for a more niche audience:

1. Transpose matrix (optional since it's so simple)
2. Diagonalizability flag for eigen vectors
3. Classification of matrices:
   • Rotation
   • Scale
   • Rotation + Scale
   • Reflection
   • Shear
   • Projection
   • Improper rotation (rotation + reflection)
   • Singular transformation (rank < 2)

C. Tertiary fancy information (leans more into animation features):

1. Polar decomposition
2. SVD (singular values + directions)

Describe alternatives you've considered

The alternative to this is to not add any of the above, but that'd be a waste of potential. There will be sub-issues to separate this into manageable chunks.

Additional context

• These bits of information would really help increase the utility of this otherwise plainly-visual tool.
• This will require significant UI changes, mainly adding a new tab next to the "all matrices" part of the "Matrices" tab.