The directionality of thermal radiance of a homogeneous isothermal non-black plane surface is totally decided by its directional emissivity, which depends; on the complex dielectric constant and roughness of surface. It can be expressed by Lλ(θk,T) = ελ(θk)Lbλ(T). This paperproves that it is necessary to express emissivity by a matrix when a target becomes an inhomo-geneous non-isothermal open complex with complicated inner geometric structure. The matrix describes the inner radiative interaction among components accurately and also expresses its thermal radiative directionality and structural characteristics completely. Advantages of matrix expression are as follows: first, the physical mechanics of effective emissivity of an open complex is described in a simple and perfect way; second, it becomes easy to understand the principle and method to retrieve components temperature from multi-angle thermal remotely sensed data; and third, the differences of directionalities between an open complex and a The directionality of thermal radiance of a homogeneous isothermal non-black plane surface is totally decided by its directional emissivity, which depends; which depends; on the complex dielectric constant and roughness of surface. It can be expressed by Lλ (θk, T) = ελ (θk This paperproves that it is necessary to express emissivity by a matrix when a target becomes an inhomo-geneous non-isothermal open complex with complicated inner geometric structure. The matrix describes the inner radiative interaction among components accurately and also expresses its thermal radiative directionality and structural characteristics completely. Advantages of matrix expression are follows: first, the physical mechanics of effective emissivity of an open complex is described in a simple and perfect way; second, it becomes easy to understand the principle and method to retrieve components temperature from multi-angle thermal remotely sensed data; and third, the differences of directionalities between an open complex and a