New Page

• Identity Matrix

  • Does nothing when applied to a vector.

  • Basis for understanding other transformations.

  • Represents standard world coordinates.

• Uniform Scaled Matrix

  • Modify all diagonal values equally.

  • Scales objects equally in all directions.

  • E.g., 0.5 on all diagonal entries = mesh is scaled down by half.

• Axis Scaled Matrix

  • Change individual diagonal values independently.

  • Scales the object along specific axes.

  • E.g., a 3 in the X-axis = stretches object 3x in X only.

• Mirror (Reflection) Matrix

  • Multiply a diagonal entry by -1 to mirror on that axis.

  • E.g., -1 in X = flips mesh on the X-axis.

• Matrix with Normalized Basis

  • Basis vectors (matrix columns) are unit length and orthogonal.

  • Often used for pure rotation without scaling.

  • Each axis remains perpendicular and consistent in size.

• Matrix with Non-Orthogonal Basis

  • Columns are not perpendicular.

  • Causes skewing—object axes are no longer at right angles.

• Matrix with Non-Normalized Basis

  • Basis vectors may differ in length.

  • Can scale along arbitrary axes (not just X, Y, Z).

• Rotation Matrices

  • Represented by changing off-diagonal values (not just diagonal).

  • Rotate vectors in space while maintaining their magnitude.

• Matrix Interpretation Tip

  • Think of each matrix column as defining a new space axis.

  • Multiplying a vector by a matrix expresses it in that new space.

Let me know if you’d like a diagram or Unity version of any of these!