User Michael Hoppe

59 votes

Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue.

linear-algebra

answered Sep 24, 2013 at 15:00

33 votes

Is it faster to count to the infinite going one by one or two by two?

elementary-set-theory

answered Feb 3, 2014 at 10:31

24 votes

Why can't $|x-2|$ be less than zero?

answered Nov 20, 2021 at 12:27

21 votes

How to find the orthogonal complement of a subspace?

vector-spaces orthogonality

answered Apr 13, 2015 at 11:30

20 votes

Accepted

Calculating limit of definite integral

limits definite-integrals

answered Jan 31, 2019 at 16:24

19 votes

A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.

calculus real-analysis

answered Apr 16, 2015 at 8:54

16 votes

Continuous injective map is strictly monotonic

real-analysis

answered Sep 14, 2015 at 13:51

13 votes

Accepted

Differences between infinite-dimensional and finite-dimensional vector spaces

linear-algebra abstract-algebra vector-spaces big-list

answered Oct 10, 2013 at 12:32

11 votes

Accepted

Algebraic Basis vs Hilbert basis

linear-algebra real-analysis

answered Nov 2, 2013 at 8:48

11 votes

Two numbers equality formula

functions

answered Oct 27, 2015 at 13:27

10 votes

Finding the limit of $\frac{\sqrt{x}}{\sqrt{x}+\sin\sqrt{x}}$

calculus limits

answered Oct 16, 2013 at 16:02

10 votes

What is the relationship between blue area and red area?

geometry euclidean-geometry recreational-mathematics area

answered Mar 19, 2018 at 11:20

9 votes

Eigenvectors are linearly independent?

linear-algebra matrices vector-spaces eigenvalues-eigenvectors

answered Dec 3, 2013 at 1:38

9 votes

Are there mathematical concepts that exist in dimension $4$, but not in dimension $3$?

geometry soft-question big-list philosophy

answered Sep 5, 2019 at 18:33

8 votes

Explain why perpendicular lines have negative reciprocal slopes

education

answered Oct 9, 2013 at 9:57

8 votes

Accepted

Crazy calculation for winding numbers

complex-analysis

answered Mar 8, 2014 at 14:05

8 votes

What is the intuitive interpretation of the transpose compared to the inverse?

linear-algebra matrices inverse intuition transpose

answered May 15, 2018 at 15:47

7 votes

Accepted

Intuition behind Variance formula

probability probability-distributions intuition

answered Mar 5, 2014 at 11:34

7 votes

The n-th root of a prime number is irrational

real-analysis prime-numbers irrational-numbers

answered Oct 30, 2013 at 11:13

7 votes

Prove that $A\mathbf{x}=0$ has a non-zero solution $\mathbf{x}$ iff $\det(A)=0$.

linear-algebra matrices eigenvalues-eigenvectors determinant

answered Sep 28, 2015 at 22:27

7 votes

Accepted

Show that $f(x)=\sqrt 2$ has no solutions $f(x)=\sin x\cos x(2+\sin x)$ and $x\in [0,\frac{\pi}{2}]$.

calculus derivatives trigonometry

answered Jun 21, 2020 at 17:23

7 votes

When a spade is not a spade

terminology education big-list

answered Sep 17, 2020 at 10:45

6 votes

How can $|x|= -x$, when $x<0$?

algebra-precalculus

answered Oct 25, 2013 at 10:44

6 votes

Reflexivity: How can something be related to itself?

elementary-set-theory terminology intuition relations

answered Oct 8, 2013 at 13:30

6 votes

$2\times2$ matrices are not big enough

linear-algebra matrices soft-question education

answered Nov 23, 2013 at 12:59

6 votes

Show that $SO(3)$ is compact.

general-topology compactness

answered Nov 8, 2013 at 7:06

6 votes

Instance of Mean Value Theorem

calculus analysis exponential-function

answered Sep 23, 2015 at 8:31

6 votes

What exactly is a matrix?

linear-algebra matrices soft-question

answered May 15, 2018 at 20:09

6 votes

Accepted

When sum of two Poisson variables is not Poisson

probability poisson-distribution

answered Apr 19, 2018 at 16:01

5 votes

Accepted

How do I solve a derivative that has an absolute value $x \times |x|$

calculus derivatives

answered Oct 15, 2013 at 13:09

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1,164 Answers

Show that a matrix $A$ is singular if and only if $0$ is an eigenvalue.

Is it faster to count to the infinite going one by one or two by two?

Why can't $|x-2|$ be less than zero?

How to find the orthogonal complement of a subspace?

Calculating limit of definite integral

A continuous, injective function $f: \mathbb{R} \to \mathbb{R}$ is either strictly increasing or strictly decreasing.

Continuous injective map is strictly monotonic

Differences between infinite-dimensional and finite-dimensional vector spaces

Algebraic Basis vs Hilbert basis

Two numbers equality formula

Finding the limit of $\frac{\sqrt{x}}{\sqrt{x}+\sin\sqrt{x}}$

What is the relationship between blue area and red area?

Eigenvectors are linearly independent?

Are there mathematical concepts that exist in dimension $4$, but not in dimension $3$?

Explain why perpendicular lines have negative reciprocal slopes

Crazy calculation for winding numbers

What is the intuitive interpretation of the transpose compared to the inverse?

Intuition behind Variance formula

The n-th root of a prime number is irrational

Prove that $A\mathbf{x}=0$ has a non-zero solution $\mathbf{x}$ iff $\det(A)=0$.

Show that $f(x)=\sqrt 2$ has no solutions $f(x)=\sin x\cos x(2+\sin x)$ and $x\in [0,\frac{\pi}{2}]$.

When a spade is not a spade

How can $|x|= -x$, when $x<0$?

Reflexivity: How can something be related to itself?

$2\times2$ matrices are not big enough

Show that $SO(3)$ is compact.

Instance of Mean Value Theorem

What exactly is a matrix?

When sum of two Poisson variables is not Poisson

How do I solve a derivative that has an absolute value $x \times |x|$