Is my lookAt function right?

OpenGL OpenGL: Basic Coding
1

The title says it all I just need some feedback if my lookAt function is correct.

mat4 mat4::view(vec3 cameraVector, vec3 targetPos,  vec3 rightVector, vec3 upVector)
	{
		mat4 result;
		mat4 secondMatrix(1.0f);
		mat4 firstMat(1.0f);
		vec3 directionVector = vec3::normalize(cameraVector - targetPos);
		
		firstMat.elements[0] = rightVector.x;
		firstMat.elements[1] = rightVector.y;
		firstMat.elements[2] = rightVector.z;
		firstMat.elements[4] = upVector.x;
		firstMat.elements[5] = upVector.y;
		firstMat.elements[6] = upVector.z;
		firstMat.elements[8] = directionVector.x;
		firstMat.elements[9] = directionVector.y;
		firstMat.elements[10] = directionVector.z;

		secondMatrix.elements[3] = -cameraVector.x;
		secondMatrix.elements[7] = -cameraVector.y;
		secondMatrix.elements[11] = -cameraVector.z;

		result = firstMat * secondMatrix;

		return result;
	}
2

Nope.

A lookAt function would be expected to generate an orthogonal matrix, so the three vectors should be perpendicular.

Typically, you would set Z to directionVector but calculate X and Y as X=normalize(cross(upVector, Z)), Y=cross(Z, X). There’s no need for rightVector.

Also, you’re storing the axes as columns, when they should be rows.

See the gluLookAt reference page for more information.