D H said:The vertices are points in ℝN2 space.
D H said:A 2x2 matrix has four elements, in this case, four real numbers. That maps to R4, so they are represented by points in 4-space.
Office_Shredder said:Usually if you have a matrix you just read it off from left to right, top to bottom. So the matrix
1 0
0 1
would be (1,0,0,1) and the matrix
0 1
1 0
would be (0,1,1,0). Of course it doesn't matter which order you put the entries of your matrix as long as you're consistent the whole time
A matrix indicates a point by using its rows and columns to represent the coordinates of the point. The first row corresponds to the x-coordinate, the second row corresponds to the y-coordinate, and the third row corresponds to the z-coordinate. The numbers in each column represent the magnitude and direction of each coordinate.
Using a matrix to indicate a point allows for mathematical operations, such as translation, rotation, and scaling, to be applied to the point. This makes it easier to manipulate and transform points in a 3D space.
Yes, a matrix can indicate a point in a 2D space by using a 3x3 matrix with the third row and column being set to 0 and 1 respectively. This essentially ignores the z-coordinate and allows for points to be represented in a 2D space.
A matrix can be used to indicate multiple points by creating a larger matrix with each column representing the coordinates of a different point. This allows for multiple points to be transformed simultaneously using the same matrix.
A matrix and a point in a 3D space are closely related as the matrix provides a way to represent and manipulate the point's coordinates. The matrix essentially acts as a transformation that can be applied to the point to change its position, orientation, or size in the 3D space.