Euclidean space as a vector space
- On the first page of simulation, first step is to choose a point on plane. Given a pair of axes, there is a corresponding point in R2. It is provided in Step 2 on the same page.
- On the same page, Step 3 provides the vector representation of the point in R2 corresponding to the chosen point in the plane in Step 1.
- This provides mathematical model for the plane as given below these steps.
- Press “Next” to go to the next page to understand 2- dimensional Euclidean space.
- On this page, underlying set is provided. To understand operations “Addition” and “Scalar Multiplication” on this set, choose the requisite tab. By default, “Addition ” appears.
- If you choose “Addition ”, enter the values to choose two points in R2. Press “Submit” button. Geometric visualization of the chosen points and their sum is provided in the next box while vector representation is provided in the third box.
- If you choose “Scalar Multiplication”, enter the values to choose a scalar and a point in R2. Press “Submit” button. Geometric visualization of the chosen points and their scalar multiplication is provided in the next box while vector representation is provided in the third box.
- Press “Previous” button to go to the previous page.
- Press “Next” button to go to the next page i.e., page 3 to understand n-dimensional Euclidean space as a vector space.
- Select desired value of n by pressing the appropriate tab to understand the Euclidean space for different values on n. By default, “n=1” appears.
- Go through the definition of n-dimensional Euclidean space as a vector space given at the end.