Matrix: This mode shows matrices, and has two modes of its own; draw, and multiply. The determinant is how much the area of the square is multiplied after the transformation, and the trace is the sum of the diagonals. Draw: The grid is made of the square before the transformation, and the shape with the thick outline is the square after the transformation. An eigenvalue is the factor by which the length of an eigenvector changes after the transformation. An eigenvector is a vector which does not change direction after the transformation. This also shows the inverse matrix as the thin line, and if it goes off to infinity, it is likely undefined. The inverse of a matrix is a matrix such that, if multiplied by the original, will give the identity matrix [[1,0],[0,1]]. A matrix and its inverse will always commute. Multiply: Multiply does matrix multiplication on A and B, giving a matrix that, if applied on a vector, would be like if you applied B and then A. The thick line is A, the medium line is B, and the thin line is A×B. Matrix multiplication is non-commutative, which means that A×B does not always equal B×A. However, it is associative, which means that A×(B×C)=(A×B)×C. Vector: This mode multiplies a vector by a matrix, giving a new vector that has undergone whats called a matrix transformation or linear transformation. Below the determinant, the matrix is shown. The vector before the transformation is the red line, the vector after the transformation is the green line, and the matrix is represented near the vectors.
Press h to hide the matrix and the vectors. Press c to unhide them. Don't make the matrix too large, or it will glitch, especially if you are using multiply mode.
