It generally makes no sense to add a scalar to a vector or to subtract a scalar from a vector. If z happens to be a complex number, then the expression ##z - 1## is treating 1 as also being a complex number (i.e., 1 + 0i), so both z and 1 are essentially vectors.Aristarchus_ said:Homework Statement:: If we have a vector z, what does it mean to subtract a value of 1 from it? What is the geometric interpretation of this?
Relevant Equations:: z-1
d
It means that you add two numbers, ##z## and ##1.##Aristarchus_ said:Homework Statement:: If we have a vector z, what does it mean to subtract a value of 1 from it? What is the geometric interpretation of this?
Relevant Equations:: z-1
d
To subtract a value from a vector, you simply need to subtract the value from each element in the vector. For example, if you have a vector [1, 2, 3] and you want to subtract 1 from it, the resulting vector would be [0, 1, 2].
Yes, you can subtract a vector from another vector by subtracting the corresponding elements from each other. For example, if you have two vectors [1, 2, 3] and [4, 5, 6], the resulting vector would be [-3, -3, -3].
If the vector and value have different dimensions, the subtraction cannot be performed. The dimensions of both must match in order for the subtraction to be valid.
Subtracting a value from a vector does not affect the direction of the vector. It only changes the magnitude of the vector. The direction remains the same.
No, subtracting a value from a vector and scaling a vector are two different operations. Subtracting a value changes the magnitude of the vector, while scaling a vector changes both the magnitude and direction.