Partial isometry
A partial isometry is like a magician who can make some things disappear and some things stay. Imagine you have a toy box with different kinds of toys inside. A partial isometry is a toy box opener who can take out some toys and make them disappear, but keep other toys in the box.
For example, let's say you have a toy box with three toys: a red ball, a blue car, and a green dinosaur. A partial isometry can open the box and take out the red ball, and make it disappear. But the blue car and green dinosaur can stay inside the box.
In math, a partial isometry is a special kind of function that can transform some parts of a space, while leaving other parts unchanged. It's like a function that can selectively apply its magic to some parts of the space.
Why is this useful? Well, in certain mathematical problems, we want to transform some parts of the space, while keeping other parts fixed. For example, imagine you have a graph with different nodes and edges, and you want to find a way to move certain nodes without changing the overall structure of the graph. A partial isometry can be used to do this kind of transformation.
So, a partial isometry is like a toy box opener with magical powers who can selectively remove some toys, while keeping others safe. In math, it's a function that can transform some parts of a space, while leaving others fixed.
For example, let's say you have a toy box with three toys: a red ball, a blue car, and a green dinosaur. A partial isometry can open the box and take out the red ball, and make it disappear. But the blue car and green dinosaur can stay inside the box.
In math, a partial isometry is a special kind of function that can transform some parts of a space, while leaving other parts unchanged. It's like a function that can selectively apply its magic to some parts of the space.
Why is this useful? Well, in certain mathematical problems, we want to transform some parts of the space, while keeping other parts fixed. For example, imagine you have a graph with different nodes and edges, and you want to find a way to move certain nodes without changing the overall structure of the graph. A partial isometry can be used to do this kind of transformation.
So, a partial isometry is like a toy box opener with magical powers who can selectively remove some toys, while keeping others safe. In math, it's a function that can transform some parts of a space, while leaving others fixed.