Projection (linear algebra)

Projection in linear algebra is like showing a movie on a screen. Imagine watching a movie about a car race. The movie is like a vector, which is a fancy word for a way of showing a direction and a length. The car race movie is projected on the screen so we can see what is happening in the movie.

Now let's pretend we only want to see the cars moving in a straight line. To do this, we need to make a special type of projection. We can use a camera to capture only the cars moving in a straight line on the screen. This is like taking a vector and projecting it onto a line.

When we project a vector onto a line, we create a new vector that is like the old one but pointing in the direction of the line. This new vector is shorter or longer than the old one depending on how much of it is pointing in the direction of the line.

In summary, projection in linear algebra is like showing a movie on a screen, but with math. We can project a vector onto a line and create a new vector that only points in the direction of the line. It's like taking a picture of the cars moving in a straight line, but with math instead of a camera.