Minor matrix

Minor sounds mysterious, doesn't it? But in fact, everything is simple. Imagine the matrix. Now remember the school "mechanics" — you remove a row and a column from it, and in place of the hole you get a submatrix. Its determinant is the very minor.

In the CalculationLaboratory, all this is done in one short line:

mn = minor(matrix, x, y);

Everything is clean here: you pass the matrix and the coordinates of the element that you are cutting out the row and column from (numbering, by the way, from scratch). The program will give you back the "dirty work" — ready minor.

Why do you need it at all, you ask? A lot of places:

If you want to solve a system of linear equations beautifully, study Kramer's method. And there are solid minors.

Need to understand the rank of the matrix? There's nowhere without minors: look at the size of the largest nonzero minor — that's the answer.

Are you working with inverse matrices? The minors are back in action. Each element of the inverse matrix is almost a separate mini—drama, with rows/columns being cut out and signs being turned over.

By and large, a minor is like a Swiss army knife for linear algebra. It's a small tool, but it saves you in a dozen tasks. Optimization, statistics, graphs, calculations — everything where you work with matrices seriously, at an early or late hour, a minor will call. And no, it's not a pun.

So, if you used to find the minors somewhat academic and boring, it's time to get to know each other better. Especially when the syntax is like this: one line, and the whole theory works for you.