We should call arrays as vector, as a list that has one dimension. It is a row of data. An array is a list that is arranged in multiple dimensions. A two-dimensional array is a vector of vectors that are all of the same length. There are nxn and nxm arrays.
currently
We can store an integer in a 1x1 vector > 12 b !
We can save a 1x3 vectors to a variable > [1 2 3] a !
We can > 1a! 3b! ab+. gives 4
We can recall values from vector with variable n? like > a 1?. gives 2
But we lack basic operations on 1xn vectors plus + and minus -
Perhaps > [1 2 3]a! [1 2 3]b! ab+ c!
then c . gives [2 4 6] rather than each number on stack. not sure
Products
More advanced maybe outside of MINT is products
/ Divide is avoided see notes below
cross product ** // transpose needed, maybe > [1 2 3 t ]
dot product * // transpose not needed
> [1 2 3]a! [1 2 3 t ]b! ab * c! c .
14
> ab d* c! c.
0
> [1 2 3]a! [4 5 6 ]b! ab ** c! c.
[ -3 6 -3]
>
Vector-variables
We can nest arrays in arrays [ n n [ m m ] n ]
but variables cannot be placed in an array. [ a b [ 3 5 ] 7 ]
If we could then we can do more
> [1 2 a 4]b!
> 3a! b.
[1 2 3 4]
>
but how do we handle + and - with var in [ ] ?
Notes on /
Primary reason we don't use the division operator / for vectors is the non-commutativity of vector multiplication.
Vector Multiplication:
Dot product: Produces a scalar (a number).
Cross product: Produces a vector perpendicular to both original vectors.
Non-Commutativity:
Dot product: Commutative (a · b = b · a).
Cross product: Non-commutative (a × b ≠ b × a).
Division:
Division is essentially the inverse of multiplication.
Since vector multiplication is non-commutative, it's difficult to define a consistent and meaningful inverse operation.
We should call arrays as vector, as a list that has one dimension. It is a row of data. An array is a list that is arranged in multiple dimensions. A two-dimensional array is a vector of vectors that are all of the same length. There are nxn and nxm arrays.
currently We can store an
integerin a 1x1 vector> 12 b !We can save a 1x3 vectors to a variable> [1 2 3] a !We can> 1a! 3b! ab+.gives 4 We can recall values from vector withvariable n?like> a 1?.gives 2But we lack basic operations on 1xn vectors
plus + and minus -Perhaps> [1 2 3]a! [1 2 3]b! ab+ c!then
c .gives [2 4 6] rather than each number on stack. not sureProducts More advanced maybe outside of MINT is products
/Divide is avoided see notes below cross product**// transpose needed, maybe> [1 2 3 t ]dot product*// transpose not neededVector-variables We can nest arrays in arrays
[ n n [ m m ] n ]but variables cannot be placed in an array.[ a b [ 3 5 ] 7 ]If we could then we can do morebut how do we handle + and - with var in [ ] ?
Notes on
/Primary reason we don't use the division operator/for vectors is the non-commutativity of vector multiplication.Vector Multiplication: Dot product: Produces a scalar (a number). Cross product: Produces a vector perpendicular to both original vectors.
Non-Commutativity: Dot product: Commutative
(a · b = b · a).Cross product: Non-commutative(a × b ≠ b × a).Division: Division is essentially the inverse of multiplication. Since vector multiplication is non-commutative, it's difficult to define a consistent and meaningful inverse operation.