Need help for transform of spherical harmonics

[xiasun]

Is there a source for this generation? The sh11, sh12, and sh13 can be somewhat confusing. Why do we need this conversion instead of using the tempMatrix3 directly?

/// SplatBuffer.js
if (transform && outSphericalHarmonicsDegree >= 1) {
    tempMatrix4.copy(transform);
    tempMatrix4.decompose(tempTranslation, tempRotation, tempScale);
    tempRotation.normalize();
    tempMatrix4.makeRotationFromQuaternion(tempRotation);
    tempMatrix3.setFromMatrix4(tempMatrix4);
    set3(sh11, tempMatrix3.elements[4], -tempMatrix3.elements[7], tempMatrix3.elements[1]);
    set3(sh12, -tempMatrix3.elements[5], tempMatrix3.elements[8], -tempMatrix3.elements[2]);
    set3(sh13, tempMatrix3.elements[3], -tempMatrix3.elements[6], tempMatrix3.elements[0]);
}

Thank you!