mercuryman said:Hey
This is from Numerical analysis course (Legendre polynom) - they gave us the polynomial transformation from [-1,1] to [a,b] as: x = 2/(b-a) * z - (b+a)/(b-a)
what is the proof of this tranformation? where did it come from?
thanks
A linear transformation is a mathematical function that maps points from one n-dimensional space to another n-dimensional space while preserving the linear structure of the original space. In simpler terms, it is a transformation that preserves the straightness and direction of lines.
The domain of a linear transformation from [-1,1] to [a,b] is the interval [-1,1], and the range is the interval [a,b]. This means that any input value between -1 and 1 will be transformed into an output value between a and b.
A linear transformation from [-1,1] to [a,b] can be represented using a linear equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept. The values of m and b will determine the specific transformation from the interval [-1,1] to [a,b].
The interval [-1,1] represents the input values of the transformation, while [a,b] represents the corresponding output values. The interval [-1,1] is often used as the standard domain for linear transformations, and the range [a,b] can be adjusted to fit the specific needs of the transformation.
Yes, a linear transformation from [-1,1] to [a,b] can have negative values in the range [a,b]. This will depend on the values of m and b in the linear equation y = mx + b. If the slope m is negative, the transformation will result in negative values in the range [a,b].