some_matrix = matrix(1:9, 3, 3)
lower_matrix <- upper_matrix <- some_matrix
lower_matrix[upper.tri(some_matrix)] <- 0
upper_matrix[lower.tri(some_matrix)] <- 0
is_triangular_matrix(some_matrix) # TRUE
is_triangular_matrix(lower_matrix) # TRUE
is_triangular_matrix(upper_matrix) # TRUE
is_lower_triangular(some_matrix) # FALSE
is_lower_triangular(lower_matrix) # FALSE
is_lower_triangular(upper_matrix) # FALSE
is_upper_triangular(some_matrix) # FALSE
is_upper_triangular(lower_matrix) # FALSE
is_upper_triangular(upper_matrix) # FALSE
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