线性代数合同的英语

线性代数合同的英语
In linear algebra, "contract" has a specific meaning that's a bit different from its everyday use. Here, it refers to two matrices being equivalent under a similarity transformation. That's like saying two people may look different but are essentially the same under a change of clothes or hairstyle.
For matrices, this "change of clothes" is a non-singular matrix that acts as a transformation. If you multiply a matrix A by this transformation matrix P on one side and its inverse P^-1 on the other, you get a new matrix B that's "contracted" to A. They have the same essential properties, just presented in a different way.
You can think of it like two maps of the same city, one in a detailed street view and the other a more zoomed-out version. They're not identical, but they represent the same place. Similarly, matrices A and B may have different numbers in them, but they're "contractually" the same in
terms of their linear algebraic properties.
Sometimes, finding this "contract" or similarity transformation can be tricky. It's like trying to figure out what kind of filter or lens you need to see two things as equivalent. But once you find it, it's a powerful tool that can reveal hidden connections between matrices.
So in summary, when we talk about matrices being "contract" in linear algebra, we're really just saying that they're related by a similarity transformation. It's a way to see the same thing in a different way, just like looking at a city from different perspectives on a map.。