Transformation of matrix and coordinate system in Linear Algebra

Points in a space can be depicted by vectors. These points are depicted based on our self-built European space coordinate system. We can use a row vector to represent a spatial point. What should we do when we want to convert spatial coordinates? A row vector B, I can understand that the three values of IB and B are three row vectors (, 0), (, 0), (, 0, 1) the measurement of the preceding three components. Let's assume that vector M is a 3x3 vector. M is linear independent. That is to say, M has three row vectors A1, A2, A3, which are not in common, MX = B. At this time, it is a column vector of 3X1. X =

X1

Y1

Z1

MX = (A1 * X1, A2 * Y1, A3 * Z1) we can understand that the product of MX is X1 in vector A1, and Y1 in A2, the measurement on A3 is z1. in this case, MX = B, B = (B1, B2, B3), so b1 = A1 * X1, b2 = a2 * Y1, B3 =, a3 * Z1. B1, B2, B3 are the three components of X, Y, and Z in the European coordinate system. X1, Y1, and Z1 are in the coordinate systems A1, A2, and A3 (this is our custom coordinate system). That is, the coordinates of points in the European coordinate system are obtained after the X vector (also a coordinate point in the M coordinate) is left multiplied by m in the Custom space. Space coordinates are converted. If the implementation of the European coordinate transformation to the M coordinate system, can be on both sides of the same time left multiplied by a m of the inverse matrix M-1, (M-1) * m * x = (M-1) * B is X = (M-1) * B. After B is used, X can be obtained, and then the coordinate of point X in the M coordinate system can be obtained.

Transformation of matrix and coordinate system in Linear Algebra