Deeper

Lab · c07.s03.L1

Matrix grid mover

A two-by-two matrix sends the two unit arrows to its two columns, and sends every other vector to x copies of the first column plus y copies of the second.

Question: What does a matrix do to a vector, and why do its two columns determine the answer?

Matrix grid moverA square grid of navy lines, origin at the centre. A gold arrow swings to the first column of a 2 by 2 matrix, (2.00, 1.00), and a dashed gold arrow to the second, (1.00, 3.00); the grid shears with them and straight lines stay straight. A russet arrow from the origin moves to the image of the vector (1.00, 1.00), the point (3.00, 4.00): one copy of the first column plus one copy of the second.A matrix is a machineoriginThe matrixA =2113The two columnsfirst column (2.00, 1.00)second column (1.00, 3.00)Where the vector goesx = 1, y = 1x times column 1 = (2.00, 1.00)y times column 2 = (1.00, 3.00)image = (3.00, 4.00)Lattice spacing 1, extent 5
Schematic Schematic: the grid, the unit arrows and the image vector are drawn to show that a matrix is fixed by its two columns. Nothing is measured. The frames show the move from the untouched grid to the grid sent to the columns (2.00, 1.00) and (1.00, 3.00), then the two column copies and their sum (3.00, 4.00).
Lab controls
2 matrix entry

Arrow keys step, Page Up/Down page, Home/End to the ends

1 matrix entry

Arrow keys step, Page Up/Down page, Home/End to the ends

1 matrix entry

Arrow keys step, Page Up/Down page, Home/End to the ends

3 matrix entry

Arrow keys step, Page Up/Down page, Home/End to the ends

1 coordinate

Arrow keys step, Page Up/Down page, Home/End to the ends

1 coordinate

Arrow keys step, Page Up/Down page, Home/End to the ends

1 fraction of the move

Arrow keys step, Page Up/Down page, Home/End to the ends

1200 ms per frame

Arrow keys step, Page Up/Down page, Home/End to the ends

Frame 1 of 10: Before the matrix movesAt the start the grid is square and the two gold arrows are the unit arrows (1.00, 0.00) and (0.00, 1.00). The russet arrow is the vector (1.00, 1.00). Nothing has been applied yet.

Keyboard: Space plays or pauses, Left and Right step, Home goes to the first frame, End goes to the last frame.

Text description of this lab

A square grid of navy lines, origin at the centre. A gold arrow swings to the first column of a 2 by 2 matrix, (2.00, 1.00), and a dashed gold arrow to the second, (1.00, 3.00); the grid shears with them and straight lines stay straight. A russet arrow from the origin moves to the image of the vector (1.00, 1.00), the point (3.00, 4.00): one copy of the first column plus one copy of the second.

Return to the section that hosts this lab

Caption status: schematic. Every lab declares one of published, re-simulated, schematic, synthetic or interpolated.