Consider matrices X and D as in Capelli's identity, i.e. with elements and at position (ij).
Let z be another formal variable (commuting with x). Let A and B be some matrices which elements are complex numbers.
Here the first determinant is understood (as always) as column-determinant of a matrix with non-commutative entries. The determinant on the right is calculated as if all the elements commute, and putting all x and z on the left, while derivations on the right. (Such recipe is called a Wick ordering in the quantum mechanics).
Read more about this topic: Capelli's Identity, Generalizations, The Mukhin–Tarasov–Varchenko Identity and The Gaudin Model
Other articles related to "statement, statements":
... One mistake is "message-hunting" — looking only for a profitable statement or idea in a poem ... A short prose statement can work better than a poem for communicating advice ... combine the first two, defining poetry as the "beautiful statement of some high truth", or "truth" with "decorations" ...
... words, if A requires B, it requires any true statement ... Thus, if at least one statement ought be true, every statement must materially entail it ought be true, and so every true statement ought be true ... if some statement ought be true then all statements that ought be true are true), consider the following logic ((U → !A) (A → ∩)) → (U ...
... C has two types of selection statements the if statement and the switch statement ... The if statement is in the form if () else In the if statement, if the in parentheses is nonzero (true), control passes to ... The switch statement causes control to be transferred to one of several statements depending on the value of an expression, which must have integral type ...
... The speech-act particle – this occurs at the beginning of the sentence and marks it as either a statement (bíi), a question (báa), et cetera in connected speech or writing, this particle is ... The evidence particle – this occurs at the end of statements and indicates the trustworthiness of the statement ... in Láadan Láadan literal translation idiomatic translation bíi ril áya mahina wa statement present-tense beautiful/beautify flower observed-truth The flower is beautiful b ...
... Jump statements transfer control unconditionally ... There are four types of jump statements in C goto, continue, break, and return ... The goto statement looks like this goto The identifier must be a label (followed by a colon) located in the current function ...
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