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Operations between vectors and vectors are carried out between each pair of corresponding vector values. The result is another vector. Thus :
...
Z
...
=
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X+Y
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is equivalent to :
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for each
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value
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i
...
Zi
...
=
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Xi
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+
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Yi
If one operand is a scalar and the other a vector, the operation is carried out between each vector value and the scalar. The result is another vector. Thus :
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Z
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=
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X+n
is equivalent to :
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for
...
each
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value i
Zi
...
=
...
Xi
...
+
...
n
...
The same logic applies to functions. If the argument of a function is a vector, the result is a vector where each element is the result of the function at the corresponding element in the input vector. Thus :
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Z
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=
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f(X)
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is equivalent to :
for each value i Zi = f(Xi)
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