Matrix: it refers to all other elements apart from the element to be analyzed. Constituent elements vary in kind and concentration, leading to existence of various matrices which require different level of characteristic X-rays. Matrix effects is the main source of analytical error. You can find more in the following:

For better understanding, let’s say a sample contains element A, B, C and some light elements. A  is the element to be analyzed. B and C are A’s adjacent elements. When given a certain intensity of X-ray, B emits its characteristic X-ray (BK) which is strong enough to excite A due to its smaller atomic number than B’s. Given C’s atomic number being smaller than A’s, the characteristic X-ray (AK) emitted from A can also excite C. There is a fat chance that the two characteristic X-rays can work for the light elements because of their way too small atomic number. So let’s not take them into consideration. In this connection, we sum up several factors that can affect the intensity of A’s characteristic X-ray.

1) Photo-electric Effect can be defined as such when AK is emitted from A which is applied a certain amount of X-ray.

2) Absorption Effect can be defined as such when some amount of AK is used to excite C.

3) Secondary X-ray can be defined as such when additional AK is generated by BK exciting A.

4) The chance to excite A gets smaller when some amount of X-ray excite B and C.

5) Compton Effect may occur in the interaction between the X-ray and light elements. This effect can cause X-ray to suffer some energy, which may or may not excite A, B and C.

Matrix Effects consist of absorption, enhancement an dispersion effect. The five points are just a simple summary as oppose to way more complex reality.