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at-tinkutara-there-are-major-bugs-with-combining-brackets-e-g-typing-A-B-T-writing-A-then-changing-it-to-A-causes-odd-size-glitches-furthermore-while-typing-my-p

Question Number 11218 by FilupS last updated on 17/Mar/17 $$\mathrm{at}\:\mathrm{tinkutara} \\ $$$$\: \\ $$$$\mathrm{there}\:\mathrm{are}\:\mathrm{major}\:\mathrm{bugs}\:\mathrm{with}\:\mathrm{combining} \\ $$$$\mathrm{brackets}. \\ $$$$\: \\ $$$$\mathrm{e}.\mathrm{g}.\:\mathrm{typing}: \\ $$$$\mid{A}\rangle=\left(\mid{B}^{\ast} \rangle\right)^{\mathrm{T}} \\ $$$$\:…

e-i-i-N-e-i-is-a-basis-vector-A-C-n-A-i-N-e-i-A-i-A-1-A-2-A-n-A-B-B-T-A-B-

Question Number 11217 by FilupS last updated on 17/Mar/17 $$\exists{e}_{{i}} :{i}\in\mathbb{N}\:\:\:\:\:\:\:\:{e}_{{i}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{basis}\:\mathrm{vector} \\ $$$$\boldsymbol{{A}}\in\mathbb{C}^{{n}} \\ $$$$\boldsymbol{{A}}=\underset{{i}\in\mathbb{N}} {\sum}{e}_{{i}} {A}_{{i}} =\begin{pmatrix}{{A}_{\mathrm{1}} }\\{{A}_{\mathrm{2}} }\\{\vdots}\\{{A}_{{n}} }\end{pmatrix}\:\:\:=\:\mid{A}\rangle \\ $$$$\langle{B}\mid=\left(\mid{B}^{\ast} \rangle\right)^{\mathrm{T}}…

Question-142252

Question Number 142252 by Algoritm last updated on 28/May/21 Answered by MJS_new last updated on 29/May/21 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{for}\:{x}\:\mathrm{then}\:\mathrm{insert}\:\mathrm{into}\:\mathrm{the}\:\mathrm{1}^{\mathrm{st}} \\ $$$$\mathrm{let}\:{y}=\mathrm{2arctan}\:{t} \\ $$$$\mathrm{solve}\:\mathrm{for}\:{t} \\ $$$$\mathrm{check}\:\mathrm{all}\:\mathrm{solutions} \\…

f-is-an-endomorphism-of-V-such-that-f-f-Id-V-1-Show-that-f-is-an-isomorphism-of-V-and-express-f-1-in-function-of-f-2-show-that-0-is-the-one-invariant-vector-by-f-3-Given-u-0-and-

Question Number 142236 by mathocean1 last updated on 28/May/21 $$\mathrm{f}\:\mathrm{is}\:\mathrm{an}\:\mathrm{endomorphism}\:\mathrm{of}\:\mathrm{V}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{f}\circ\mathrm{f}=−\mathrm{Id}_{\mathrm{V}} \:. \\ $$$$\mathrm{1}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{f}\:\mathrm{is}\:\mathrm{an}\:\mathrm{isomorphism}\:\mathrm{of} \\ $$$$\mathrm{V}\:\mathrm{and}\:\mathrm{express}\:\mathrm{f}^{−\mathrm{1}} \:\mathrm{in}\:\mathrm{function}\:\mathrm{of}\:\mathrm{f}. \\ $$$$\mathrm{2}.\:\mathrm{show}\:\mathrm{that}\:\overset{\rightarrow} {\mathrm{0}}\:\mathrm{is}\:\mathrm{the}\:\mathrm{one}\:\mathrm{invariant} \\ $$$$\mathrm{vector}\:\mathrm{by}\:\mathrm{f}. \\ $$$$\mathrm{3}.\:\mathrm{Given}\:\overset{\rightarrow}…