Determinant

Matrix Determinant

A scalar value computed from a square matrix that indicates whether the matrix is invertible and describes scaling.

技術的詳細

Determinant operations are fundamental to computer graphics, machine learning, and data analysis. A 4x4 transformation matrix encodes rotation, scaling, translation, and perspective in 3D graphics — CSS transforms use this internally. Matrix multiplication is not commutative (A×B ≠ B×A), which means transform order matters. GPUs are essentially parallel matrix processors, making matrix operations orders of magnitude faster on GPU than CPU for large datasets.

例

```
2x2 Matrix multiplication:

  [a b]   [e f]   [ae+bg  af+bh]
  [c d] × [g h] = [ce+dg  cf+dh]

  Example: Scaling + Rotation matrix (2D):
  [cos θ  -sin θ]   [sx  0]
  [sin θ   cos θ] × [0  sy]
```

Categories

Determinant

技術的詳細

例

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