- #1
PhizKid
- 477
- 1
Homework Statement
S = {1, x, x^2}
Find ||1||, ||x||, and ||x^2||.
Homework Equations
##\sqrt{v \cdot v}##
The Attempt at a Solution
I don't know the components of each vector, so how can I perform the dot product?
Since you ended with a question mark, you're not sure. Please show us what you did to get these, rather than making us do that work.PhizKid said:Ah, okay. So the respective lengths are just ##\sqrt{1}##, ##\sqrt{\frac{1}{3}}##, and ##\sqrt{\frac{1}{5}}##?
A polynomial vector is a mathematical object that contains a list of coefficients, each representing the value of a specific term in a polynomial equation. It can also be thought of as a one-dimensional array of numbers.
The length, or magnitude, of a polynomial vector is calculated by taking the square root of the sum of the squares of its coefficients. This is similar to how the length of a vector in traditional geometry is calculated.
The length of a polynomial vector is important because it represents the magnitude or size of the vector. This can be useful in various mathematical and scientific applications, such as calculating the distance between two vectors or determining the strength of a force represented by a vector.
No, the length of a polynomial vector cannot be negative. It is always a positive value, as it is calculated using the square root function.
The length of a polynomial vector is not affected by its dimensions. It is solely determined by the values of its coefficients, not the number of terms or dimensions in the vector.