transpose

transpose :: (matNxM m) -> matMxN {...}

pipeline NormalTransform {
  fragment {
    // Transform normal by inverse transpose of model matrix
    // For non-uniform scaling, normals need special handling
    mat3 normalMatrix = mat3(tangent, bitangent, normal);
    normalMatrix = transpose(inverse(normalMatrix));

    float3 worldNormal = normalize(normalMatrix * input.normal);

    output.color = float4(worldNormal * 0.5 + 0.5, 1.0);
  }
}

// Correct normal matrix for non-uniform scaling
mat3 normalMatrix = transpose(inverse(mat3(tangent, bitangent, normal)));
float3 worldNormal = normalize(normalMatrix * objectNormal);

// For orthonormal matrices, inverse = transpose
mat3 rotationOnly = mat3(right, up, forward);
mat3 inverseRotation = transpose(rotationOnly);

// Convert from tangent to world space (and back)
mat3 TBN = mat3(tangent, bitangent, normal);
mat3 inverseTBN = transpose(TBN);  // Works if orthonormal

// Convert between conventions
mat4 columnMajor = transpose(rowMajorMatrix);

// Change multiplication order: transpose(A * B) = transpose(B) * transpose(A)
mat3 combined = transpose(transpose(B) * transpose(A));

transpose(m)

transpose(m)