## 7 Conclusions and Future Works  
The data-hiding technique using a Hermitian positive definite matrix presents a promising approach for securely embedding sensitive information within multimedia content. By exploiting the mathematical properties of Hermitian positive definite matrices, the method achieves a balance between imperceptibility and robustness. The main takeaway from this research is the potential application of this technique in various security-sensitive domains, such as watermarking, authentication, and covert communication, where confidentiality and integrity are paramount. Our main motivation is the understanding that \"the security of the cryptosystem lies in the secret of the key\". The proposed solution features a highly robust and secure stego-key due to the vast number of combinations available with Hermitian positive definite matrices of order 8. These matrix systems are widely utilized in encryption and data-hiding techniques, including steganography. The Hermitian positive definite matrix used for calculating the weighted Moore-Penrose inverse exemplifies one of the applications of these matrices in cryptography and steganography. In both fields, the selection of Hermitian positive definite matrices is often based on their mathematical characteristics such as being Hermitian (self-adjoint) and positive definite. These traits enhance the security and reliability of the associated algorithms and techniques. However, the specific applications and techniques may vary, and researchers and practitioners in these fields continually explore new ways to leverage matrices for enhanced security and data hiding. The use of Hermitian positive definite matrices in steganography can help preserve the perceptual quality of the host media. The matrix operations, which are applied to data embedding, aim to minimize visual or auditory artifacts, ensuring that the hidden data remain imperceptible to the human senses. We leave for future research to derive other identities involving Catalan numbers and hypergeometric functions, based on the matrix products. However, further research and testing are necessary to explore its performance under various scenarios and to evaluate its resilience against advanced attacks. Future work will include a database storage system interconnected with Database Management Systems presented in [33; 34]. We leave for future research to derive other identities, which involve the generalized Catalan matrix as a kind of lower triangular Toeplitz matrix whose nonzero elements involve the generalized Catalan numbers based on the matrix products [35]. While quantum computing and quantum machine learning present new challenges for steganography, they also offer opportunities for developing more resilient techniques. By addressing these challenges through ongoing research and adaptation, the field can continue to advance in the face of emerging technologies. Our method in the future may develop in the direction of an HPD matrix approach to quantum algorithms by modeling on research [36]. The whole story could be related to quantum cryptography-steganography and blockchain technologies, as [PERSON] et al. suggested in their paper \"Quantum-Assisted Blockchain\". As quantum technologies continue to advance, the role of matrix operations in developing and refining quantum steganographic techniques will remain a critical area of research and application. Matrix calculations are integral to various aspects of quantum steganography, including the representation and manipulation of quantum states, embedding and extraction of information, and error correction. Methodology, S.P., M.S. and A.S.; Software, S.P., M.S. and D.K. ; Validation, S.P., M.S. and A.S.; Investigation, M.M., A.H. and P.B. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding authors.