[vox] OT: matrix operations

[Jeff Newmiller]

Seems more like a technical question...

Henry House wrote:
> I know about these defined arithmetic operations on vectors:
> vector addition, scalar mutiplication, and vector multiplication.
> 
> [1 2]   [4 3]   [5 4]
> [3 4] + [1 2] = [4 6]

[1 2]   [4 3]   [5 5]
[3 4] + [1 2] = [4 6]

> [1 2]           [2 4]
> [3 4] * 2     = [6 8]
> 
> [1 2]   [2 2 2]   [ 6  6  6]
> [3 4] * [2 2 2] = [14 14 14]
> 
> Why does one never hear about a scalar addition operation? It would
> make sense to me to define the following:
> 
> [1 2]       [3 4]
> [3 4] + 2 = [5 6]

Never say never.  GNU "R" will do this. In standard mathematical
notation, however, this is easily notated with

[1 2]   [1 1]     [3 4]
[3 4] + [1 1]*2 = [5 6]

so supporting this in an alternate standard notation hasn't
been necessary.

> Similarly, why is there no scalar exponentiation on vectors?

Again, "R" does this.  However, I think vectors are typically
considered special matrices, and exponentiation of matrices is
typically defined with cross product which requires compatible
dimensions (square matrices), so there is a potential
notational confusion in standard mathematical terminology.

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