/sci/ - Science & Math

>>14946287
Let A be the original matrix; let C be the square submatrix you end up with; and let B be the intermediate rectangular matrix that is as wide as C but as tall as A.

It's pretty obvious that [math]\mathrm{rk}A = \mathrm{rk}B[/math]. And since every row of A is a linear combination of basis rows, you can take these same linear combinations of the corresponding rows of B to see that [math]\mathrm{rk}B \leq \mathrm{rk}C[/math]. But we also know [math]\mathrm{rk}B \geq \mathrm{rk}C[/math] since C embeds into B, and hence they are equal.
>>14947682
>sketches, like the ones you'd make on paper
Are you asking for: a latex GUI that also near-seamlessly lets you draw with some kind of touchscreen or tablet? If so, I would also like to know.

Right now I just use MS-paint on windon'ts and Tuxpaint on GNU/Linux