Orodruin said:The matrix you quote does not map e1 to -e2. I recommend that you start by writing down the most general matrix and then see how it acts on e1 and e2 respectively. From there you can identify the elements of the matrix.
I would lend you my niece, but she turned six the day before yesterday. ;)SYoungblood said:To use your tag line, a child of five might understand this, but I am not a child of five.
A linear transformation is a mathematical operation that maps one vector space to another while preserving the basic structure of the original space. In simpler terms, it is a transformation that maintains the lines and origin of a graph.
A 2 x 2 matrix is a mathematical notation used to represent a set of numbers arranged in a rectangular array of two rows and two columns. It is often used to represent linear transformations in two-dimensional space.
To perform a linear transformation on a 2 x 2 matrix, you need to multiply the matrix by a transformation matrix, which contains the coefficients of the transformation. The resulting matrix will represent the new coordinates of each point after the transformation.
Linear transformations in 2 x 2 matrices have various applications in fields such as computer graphics, image processing, and physics. They can be used to rotate, scale, reflect, or shear objects in a two-dimensional space.
A linear transformation in a 2 x 2 matrix is invertible if its determinant is non-zero. The determinant can be calculated by multiplying the elements in the main diagonal and subtracting the product of the elements in the other diagonal. If the determinant is zero, the transformation is not invertible.