Mnemonics for linear algebra Sometimes formulas in linear algebra are not easy to remember. Some usefulness for the process of remembering can provide application of mnemonics.  


*

*Do you know some useful mnemonics for this purpose?


I'll give  two examples:


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*For the process of finding the inverse of matrix it could be used
mnemonic Detminstra what can be translated as 1. calculate
determinant 2. for every entry find minors with the sign 3. transpose obtained matrix.

*The other example is Avvedia  what is the shortcut for the formula
with eigenvectors $AV=VD$. Knowing this formula we can easily obtain
formula $A=VDV^{-1}$  or twin formula for diagonal matrix
$D=V^{-1}AV$- sometimes $V$ and $V^{-1}$ can be erroneously
interchanged - with Avvedia it is easier to check correctness of
a formula.


What other mnemonics could be useful in linear algebra?
Added lately


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*Furorri: concerning existence of right inverse for full row rank matrix (analogously for full column rank matrix would be Fucorlin) - these two inverses easy to erroneously interchange.

 A: (Too long for a comment.)
I agree with some commenters here. Before you can build up muscle memory, it is often easier, or even faster, to derive what you need than to recall mnemonics. And derivation also makes you understand better. At least this is my own experience when linear algebra is concerned.
In recent years, the only formula that I almost need some mnemonics to help remembering is the formula for calculating the determinant of a block-$2\times2$ matrix when two adjacent sub-blocks commute. Consider
$$
M=\pmatrix{A&B\\ C&D},
$$
where the four sub-blocks are square submatrices of identical sizes over some commutative ring. When some two adjacent sub-blocks of $M$ commute, we have (c.f. John Silvester, Determinants of Block Matrices)
$$
\det M=
\begin{cases}
\det(AD-BC) & \text{ if } C,D \text{ commute},\\
\det(DA-CB) & \text{ if } A,B \text{ commute},\\
\det(DA-BC) & \text{ if } B,D \text{ commute},\\
\det(AD-CB) & \text{ if } A,C \text{ commute}.
\end{cases}
$$
This is analogous to the formula $\det\pmatrix{a&b\\ c&d}=ad-bc$, but care must be taken here because the orders of $A,B,C,D$ in the polynomials above (i.e. $AD-BC$ etc.) depend on which sub-block commutes with which.
Kind of messy, right? But if you truly understand how they are derived, you don't need any mnemonics. First, we use Gaussian elimination to eliminate the off-diagonal block among the pair of commuting sub-blocks. E.g. in the first case above, i.e. when $C$ and $D$ commute, we have
$$
\pmatrix{A&B\\ C&D}\pmatrix{D&0\\ -C&I}=\pmatrix{AD-BC&B\\ 0&D}.\tag{1}
$$
Take determinants on both sides, we get $\det(M)\det(D)=\det(AD-BC)\det(D)$. Cancelling out $\det(D)$, we get the result.
At this point, the derivation still looks tedious. However, note that in our derivation, the second block column of $(1)$ does not really matter to our end result. So, to find the right polynomial we need, all we only need to calculate
$$
\pmatrix{A&B\\ C&D}\pmatrix{D\\ -C}.
$$
In other words, when we have a row of commuting sub-blocks, we use a block column vector to kill off the off-diagonal commuting block ($C$ in this example), and the only thing that you need to memorise is the following:

It is the off-diagonal commuting sub-block that has a negative sign in the killer block vector.

With this in mind, it is now dead easy to see what polynomial to use in each of the above four cases:
$$
\begin{cases}
\pmatrix{A&B\\ C&D}\pmatrix{D\\ -C}=\pmatrix{AD-BC\\ 0}
& \text{ if } C,D \text{ commute},\\
\\
\pmatrix{A&B\\ C&D}\pmatrix{-B\\ A}=\pmatrix{0\\ DA-CB}
& \text{ if } A,B \text{ commute},\\
\\
\pmatrix{D&-B}\pmatrix{A&B\\ C&D}=\pmatrix{DA-BC&0}
& \text{ if } B,D \text{ commute},\\
\\
\pmatrix{-C&A}\pmatrix{A&B\\ C&D}=\pmatrix{0&AD-CB}
& \text{ if } A,C \text{ commute}.
\end{cases}
$$
A: I made a mnemotechnic (quick and dirty attached in the image) for remembering the dimensions of the iMage space & Null space and it's relation to matrix vector multiplication of an M x N matrix. I plan on making a more beautiful LaTeX version when I find the time.
Mnemotechnic for dimensions and null space image space
(first post so link instead of image...)
