Sentence examples for points of the reflection from inspiring English sources

Then L and L ( ± b 2 ) are the lines of the eigenvectors of the matrix T and the set of the fixed points of the reflection T ( z ) is the line x = ± b 2. Proof The proof follows by Lemma 3, Lemma 4 and Lemma 5. □.

If L ( w 1 ) and L ( w 2 ) are the lines of the eigenvectors of the matrix T, then the set of the fixed points of the reflection T ( z ) is the circle centered at M ( w 1 + w 2 2, 0 ) and of radius | w 1 − w 2 | 2. Proof For the slopes w 1 = 1 − d c and w 2 = − d + 1 c, we have w 1 + w 2 2 = a c. and | w 1 − w 2 | 2 = 1 | c |. Then the proof follows by Lemma 6. □.

In the following theorem, we explain the relationship between fixed points of the reflections with c = 0 and eigenvectors of the matrices corresponding to those reflections.

In the following theorem, we explain the relationship between the set of fixed points of the reflections with c ≠ 0 and eigenvectors of matrices corresponding to those reflections.

The set of the fixed points of this reflection is the circle x = b 2. Proof The proof follows by straightforward computations.

The set of the fixed points of this reflection is the circle x = b 2.  .

As an example, it is shown in Figure 4 that for an antenna at the height of 4.3 m above the reflector, the specular point of the reflection area is located at 7.5- and 3.6-m distances from the antenna for observations from elevation angles of 30° and 50°, respectively.

The set of the fixed points of this reflection is a circle with radius ∞, that is, the line x = − b 2. The matrix T = ( − 1 b 0 1 ) represents the reflection T ( z ) = − z ¯ + b.

The set of the fixed points of this reflection is a circle with radius ∞, that is, the line x = − b 2.   (ii) The matrix T = ( − 1 b 0 1 ) represents the reflection T ( z ) = − z ¯ + b.

Now we find the fixed points of the glide reflections and reflections in the group G.

Example 1 By (2.3) we find the fixed points of the glide reflection T = ( 1 2 1 1 ) as x = ± 2. By (3.2) we find the eigenvalues as.