How do I check if a 1x1 matrix is diagonal, lower/upper triangular?

[hkBattousai]

I have an A matrix with dimensions 1x1. Its the only term a₁₁ is an arbitrary number.

For what values of a₁₁, this A matrix is;

1. Diagonal
2. Upper triangular
3. Lower triangular

 

[janvdl]

I have an A matrix with dimensions 1x1. Its the only term a₁₁ is an arbitrary number.

For what values of a₁₁, this A matrix is;

1. Diagonal
2. Upper triangular
3. Lower triangular

By definition a 1x1 matrix will be upper and lower triangular. (But not strictly; for strictly upper and lower: $a$ must be 0).

A matrix is diagonal if it is triangular and normal. Normal (for a matrix whose elements lie in the domain of real numbers) means $A \ A^T = A^T \ A$

 

[adriank]

A matrix is diagonal if it has no nonzero entries off the diagonal. A matrix is upper triangular if it has no nonzero entries below the diagonal. etc.

Clearly any 1x1 matrix satisfies these properties, since there are no entries off the diagonal, nonzero or not.