Costas arrays are permutation matrices that meet the additional Costas condition. The Costas condition requires that when a Costas array defines the frequencies in a frequency jump burst and a signal is processed with a matched filter, then for any time or Doppler offset other than both zero, only one pulse will be at peak response at a time. Specific formulations of the Costas conditions provide a vector-matrix arithmetic representation where the matrix has eigenvalues that are square roots of integers and eigenvectors that can be scaled to have elements that are all integers. Polynomials are given for squared eigenvalues and for elements of scaled right eigenvector elements. A database of these singular value decompositions is provided on IEEE DataPort for orders from 3 to 1030, with left eigenvectors to order 100. We include proofs of validity and configuration. The right eigenvectors and the eigenvalues map a Costas array vector into its eigenspace. Functions of these vectors can be associated with system performance metrics so that these mapped vectors may be used to select and rank Costas arrays and is suitable for real-time system implementation.

中文翻译：

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Costas阵列选择的Costas条件的矩阵表示的奇异值分解

Costas数组是满足附加Costas条件的置换矩阵。Costas条件要求，当Costas阵列在跳频脉冲串中定义频率并用匹配的滤波器处理信号时，对于任何时间或多普勒偏移（除了两个以外），任何时候一次只有一个脉冲处于峰值响应。Costas条件的特定公式提供了矢量矩阵算术表示，其中矩阵的特征值是整数的平方根，特征向量可以缩放为所有元素都是整数。为平方特征值和比例右特征向量元素的元素提供多项式。这些奇异值分解的数据库在IEEE DataPort上提供，其阶数为3到1030，而左特征向量为阶数100。我们包括有效性和配置证明。正确的特征向量和特征值将Costas数组向量映射到其特征空间。这些向量的功能可以与系统性能指标相关联，以便可以将这些映射的向量用于选择和排序Costas阵列，并适合于实时系统实现。