User contributions for Julius

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20:3920:39, 25 January 2024 diff hist +503‎ m User:Julius ‎No edit summary current

22:1022:10, 24 January 2024 diff hist +127‎ m Span of Exponential of a x by Cosine of b x and Exponential of a x by Sine of b x is preserved under Differentiation wrt x ‎No edit summary
22:0422:04, 24 January 2024 diff hist +256‎ m User:Julius ‎No edit summary

21:1021:10, 16 October 2023 diff hist +3,127‎ N Set of Invertible Continuous Transformations is Open Subset of Continuous Linear Transformations in Supremum Operator Norm Topology ‎ Created page with "== Theorem == Let $X$ be a Banach space. Let $\map {CL} X$ be the continuous linear operator space on $X$. Let $\map {GL} X$ denote the set of all invertible continuous linear operators on $X$. Then $\map {GL} X \subseteq \map {CL} X$ in the supremum operator norm topology...." current
21:0821:08, 16 October 2023 diff hist +131‎ m Properties of Product of Identity plus Operator Raised to Powers of 2 ‎No edit summary current

21:5221:52, 5 October 2023 diff hist +268‎ m User:Julius ‎No edit summary

10:0910:09, 28 September 2023 diff hist +443‎ m User:Julius ‎No edit summary

13:0513:05, 27 September 2023 diff hist +230‎ m User:Julius ‎No edit summary
12:1212:12, 27 September 2023 diff hist +422‎ m User:Julius ‎No edit summary
11:5811:58, 27 September 2023 diff hist +220‎ m User:Julius ‎No edit summary
11:4511:45, 27 September 2023 diff hist +183‎ m Talk:Main Page ‎No edit summary

11:0011:00, 26 September 2023 diff hist +407‎ m User:Julius ‎No edit summary
10:5210:52, 26 September 2023 diff hist +209‎ m User:Julius ‎No edit summary
10:5010:50, 26 September 2023 diff hist +153‎ m User:Julius ‎No edit summary
10:4710:47, 26 September 2023 diff hist +231‎ m User:Julius ‎No edit summary

11:2111:21, 25 September 2023 diff hist −9,331‎ m User:Julius ‎No edit summary
10:5510:55, 25 September 2023 diff hist +49‎ m Properties of Product of Identity plus Operator Raised to Powers of 2 ‎No edit summary
10:4710:47, 25 September 2023 diff hist −42‎ m Properties of Product of Identity plus Operator Raised to Powers of 2 ‎No edit summary
10:4710:47, 25 September 2023 diff hist +353‎ m Properties of Product of Identity plus Operator Raised to Powers of 2 ‎No edit summary
06:0706:07, 25 September 2023 diff hist +53‎ m Asymptotically Equal Real Functions/Examples/sin x and x ‎No edit summary

21:1121:11, 24 September 2023 diff hist +385‎ m Properties of Product of Identity plus Operator Raised to Powers of 2 ‎No edit summary
20:4420:44, 24 September 2023 diff hist −570‎ m P-Norm of Real Sequence is Strictly Decreasing Function of P ‎ Resolved current

07:4507:45, 22 September 2023 diff hist +671‎ m Definition talk:Riemannian Metric ‎No edit summary

21:3421:34, 21 September 2023 diff hist +318‎ m P-Norm of Real Sequence is Strictly Decreasing Function of P ‎ Partial resolution fixed
21:3121:31, 21 September 2023 diff hist +570‎ m P-Norm of Real Sequence is Strictly Decreasing Function of P ‎ Partial resolution
20:1320:13, 21 September 2023 diff hist +270‎ m Definition:Riemannian Metric ‎No edit summary Tag: Reverted

11:3611:36, 17 July 2023 diff hist −505‎ m Definition:Neumann Series ‎No edit summary
11:3311:33, 17 July 2023 diff hist +3,968‎ N Properties of Product of Identity plus Operator Raised to Powers of 2 ‎ Created page with "{{WIP|links, extra steps, notation etc.}} == Theorem == Let $X$ be a Banach space. Let $\map {CL} X$ be a continuous linear transformation sapce. Let $\norm {\, \cdot \,}$ be the supremum operator norm. Let $A \in \map {CL} X$ be such that $\norm A < 1$. Let $I$ be the identity mapping. Let $\circ$ be the Definiti..."
11:2811:28, 17 July 2023 diff hist +69‎ m System of Linear Equations as Continuous Linear Transformation ‎No edit summary
09:3709:37, 17 July 2023 diff hist +14‎ m System of Linear Equations as Continuous Linear Transformation ‎No edit summary
09:3309:33, 17 July 2023 diff hist +160‎ m System of Linear Equations as Continuous Linear Transformation ‎No edit summary

21:1221:12, 16 July 2023 diff hist +60‎ m System of Linear Equations as Continuous Linear Transformation ‎No edit summary
18:4218:42, 16 July 2023 diff hist +463‎ m System of Linear Equations as Continuous Linear Transformation ‎No edit summary

23:5423:54, 14 July 2023 diff hist +187‎ m Definition talk:Regular Curve ‎No edit summary current
23:5123:51, 14 July 2023 diff hist +28‎ m Definition:Differential of Mapping/Manifolds ‎No edit summary current
23:5023:50, 14 July 2023 diff hist +731‎ N Definition:Differential of Mapping/Manifolds ‎ Created page with "== Definition == {{WIP|Polishing}} Let $M$ and $N$ be smooth manifolds with or without boundary. Let $F : M \to N$ be a smooth map. Let $T_p M$ be the tangent space at $p \in M$. Then the '''differential of $F$''', denoted by $d F$, is the mapping $d F_p : T_p M \to T_{\map F p} N$ such that: :$\forall f \in \map {C^\infty} N : \forall p \in..."
23:1923:19, 14 July 2023 diff hist +1,343‎ m System of Linear Equations as Continuous Linear Transformation ‎No edit summary

08:2908:29, 13 July 2023 diff hist +190‎ m Definition talk:Regular Curve ‎No edit summary
08:2508:25, 13 July 2023 diff hist +887‎ m Definition talk:Regular Curve ‎No edit summary

19:1419:14, 12 July 2023 diff hist +372‎ m Definition talk:Regular Curve ‎No edit summary
12:1812:18, 12 July 2023 diff hist +1,924‎ m System of Linear Equations as Continuous Linear Transformation ‎No edit summary

13:2713:27, 11 July 2023 diff hist +1,355‎ m Definition talk:Regular Curve ‎No edit summary

14:2014:20, 10 July 2023 diff hist +120‎ m Definition:Regular Curve ‎No edit summary

23:3223:32, 6 July 2023 diff hist +363‎ m Talk:Neumann Series Theorem ‎No edit summary current
23:2023:20, 6 July 2023 diff hist +230‎ m Talk:Neumann Series Theorem ‎No edit summary
23:1623:16, 6 July 2023 diff hist +163‎ m Definition:Neumann Series ‎No edit summary
12:3512:35, 6 July 2023 diff hist +62‎ m Neumann Series Theorem/Corollary 2 ‎No edit summary current
12:3512:35, 6 July 2023 diff hist +1,273‎ N System of Linear Equations as Continuous Linear Transformation ‎ Created page with "== Theorem == Let $x_1, x_2 \in \R$ be real numbers. Consider the following system of simultaneous linear equations $(S)$: {{begin-eqn}} {{eqn | l = x_1 | r = \frac 1 2 x_1 + \frac 1 3 x_2 + 1 }} {{eqn | l = x_2 | r = \frac 1 3 x_1 + \frac 1 4 x_2 + 2 }} {{end-eqn}} Let $\norm {\, \cdot \,}_2$ be the $2$-norm. Let $\norm {\, \cdot \,}$ be the Definition:Suprem..."
12:1112:11, 6 July 2023 diff hist +66‎ m Neumann Series Theorem/Corollary 2 ‎No edit summary
12:1012:10, 6 July 2023 diff hist +66‎ m Neumann Series Theorem/Corollary 1 ‎No edit summary current

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