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location Florida
age 18
visits member for 1 year, 11 months
seen 18 hours ago

highschooler and recreational mathematician


Dec
14
revised Find the determinant of a matrix definition
added 1 character in body
Dec
13
reviewed Approve inverse of a point $p$ respect to the circle $|z-z_0 |= r$ in complex
Dec
13
answered Confusion about change of basis matrix
Dec
13
comment Can anyone help me with “rotation matrix” and “Image of matrix”?
if $A$ is a 'rotation' matrix it can alternatively be seen as a change of basis in which the vectors $e_1=(1,0,0),e_2=(0,1,0),e_3=(0,0,1)$ are mapped to the columns $e_1',e_2',e_3'$ of $A$
Sep
30
awarded  Explainer
Sep
24
awarded  Autobiographer
Aug
28
comment Is it possible to study information theory while studying a first course on probability?
it shouldn't necessarily hurt, but I am concerned that the rigor of the course leaves much desired in terms of intuition and understanding required to learn even basic information theory
Jul
2
awarded  Curious
Jun
2
awarded  Good Question
May
7
comment Evaluating the infinite series $\sum\limits_{n=1}^\infty(\sin\frac1{2n}-\sin\frac1{2n+1})$
@user45105 $a_k=\sin(1/(2k))\implies a_{k+1/2}=\sin(1/(2(k+1/2)))=\sin(1/(2k+1))$
May
7
comment How come $32.5 = 31.5$?
@MathGems unfortunately it is not mine.
Apr
20
awarded  Popular Question
Feb
15
awarded  Civic Duty
Feb
1
comment The strange (for me) case of Mod of Iota.
we can define $|z|$ by identifying $z\in\mathbb{C}$ with $(\Re\{z\},\Im\{z\})\in\mathbb{R}^2$ and by analogy with $|\cdot|:\mathbb{R}\to\mathbb{R}^{\ge0}$ defining it as the Euclidean distance from $(\Re\{z\},\Im\{z\})$ to $(0,0)$
Feb
1
comment The strange (for me) case of Mod of Iota.
how the hell are we cheating our way out of a paradox? there are uncountably many $z\in\mathbb{C}$ that satisfy $|z|=1$ -- consider $t\mapsto\exp(it)$. This is true. You are wrongly assuming that $|i|=1\implies i=\pm1$ holds for complex numbers when it clearly does not.
Feb
1
comment The strange (for me) case of Mod of Iota.
$|x|=1\implies x=\pm1$ is only true for $x\in\mathbb{R}$; when we generalize modulus to $\mathbb{C}$ this is no longer true as you pointed out.
Jan
25
comment Why is an orthogonal matrix called orthogonal?
the comment tells you why: they are of no particular interest... if a matrix has orthogonal columns then it necessarily is of the form $UD$ where $U$ is orthogonal and $D$ is diagonal
Jan
24
comment Why is an orthogonal matrix called orthogonal?
"It might be tempting to suppose a matrix with orthogonal (not orthonormal) columns would be called an orthogonal matrix, but such matrices have no special interest and no special name." en.wikipedia.org/wiki/Orthogonal_matrix#Matrix_properties
Jan
24
comment Is this $\epsilon-\delta-$proof correct?
(+1) exactly what I was in the midst of typing
Jan
24
comment Is this $\epsilon-\delta-$proof correct?
you can also use \operatorname{Re} i.e. $\operatorname{Re}$