Failure Rates Of The Matrix Triangle Inequality - Jime, Osman; Kaseram, Jordan (MacEwan University Student eJournal, 2024)
The triangle inequality is a fundamental principle in mathematics. However, its validity is not always guaranteed in matrix theory, specifically, when dealing with the matrix absolute value. We investigate how often the matrix absolute value satisfies the triangle inequality for different spaces of matrices. By using numerical methods, we quantify the frequency with which the triangle inequality holds and examine possible key factors contributing to its success or failure.