Are one-by-one matrices equivalent to scalars?

I am a programmer, so to me [x]x—a scalar in some sort of container is not equal to the scalar. However, I just read in a math book that for 1×1 matrices, the brackets are often dropped. This strikes me as very sloppy notation if 1×1 matrices are not at least functionally equivalent to scalars. As I began to think about the matrix operations I am familiar with, I could not think of any (tho I am weak on matrices) in which a 1×1 matrix would not act the same way as a scalar would when the corresponding scalar operations were applied to it. So, is [x] functionally equivalent to x? And can we then say [x]=x? (And are those two different questions, or are entities in mathematics “duck typed” as we would say in the coding world?)

Answer

No. To give a concrete example, you can multiply a 2×2 matrix by a scalar, but you can’t multiply a 2×2 matrix by a 1×1 matrix.

It is sloppy notation.

Attribution
Source : Link , Question Author : Kazark , Answer Author : charles.y.zheng

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