Dual-Valued Functions of Dual Matrices with Applications in Causal
Emergence
Dual-Valued Functions of Dual Matrices with Applications in Causal
Emergence
Dual continuation, an innovative insight into extending the real-valued functions of real matrices to the dual-valued functions of dual matrices with a foundation of the G\^ateaux derivative, is proposed. Theoretically, the general forms of dual-valued vector and matrix norms, the remaining properties in the real field, are provided. In particular, …