Ranks of Checkered Pattern Matrices with Applications to Information Embedding and Retrieving
Hideo Hirose
秸秃图案的特点是其方形结构和使用只有两种不同的颜色。 这些颜色通常由两种类型的数值集表示:1,0和1-1。 基于1,0的矩阵在形成检查模式时可能与基于1-1的矩阵相同,因为唯一的区别是数字0改为-1。 然而,这两种矩阵在数学意义上是完全不同的,因为使用1,0的矩阵具有2的等级,使用1-1的矩阵具有1的等级。 提前了解这种差异可以让我们减少矩阵操作所需的计算工作量,例如信息嵌入和检索。
Checkered patterns are characterized by their square structure and the use of only two distinct colors. These colors are typically represented by two types of numerical sets: 1,0 and 1,-1. Matrices based on 1,0 may seem identical to those based on 1,-1 when forming checkered patterns because the only difference is that the numbers 0 are changed to -1. However, these two kinds of matrices are completely different in a mathematical sense because a matrix using 1,0 has a rank of 2 and a matrix usin...