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14 votes

2 answers

14k views

Good books on complex numbers

asked Jun 22, 2017 at 0:58

13 votes

3 answers

873 views

Find $\lim\limits_{n \to \infty} \frac{\sqrt 1 + \sqrt 2 + \dots + \sqrt{n}}{n\sqrt{n}}$.

asked Sep 3, 2017 at 19:35

12 votes

4 answers

5k views

When are definite integrals undefined?

asked Jul 8, 2017 at 15:25

12 votes

3 answers

3k views

Determinant of a companion matrix

asked Nov 11, 2017 at 21:42

9 votes

1 answer

450 views

Computing determinant without expansion

asked Aug 14, 2017 at 16:11

8 votes

3 answers

6k views

Why discriminant of a polynomial is so special?

asked May 30, 2017 at 23:43

5 votes

1 answer

87 views

Find $\sum_{k=1}^{2n} k {2n\choose k}^2 (-1)^{k+1}$. [duplicate]

asked May 1, 2019 at 20:51

3 votes

2 answers

2k views

Prove that pivot columns of row reduced form of any matrix forms a basis in column space of that row reduced matrix.

asked Oct 26, 2017 at 15:41

3 votes

2 answers

964 views

Definition of transitivity.

asked Aug 14, 2017 at 9:01

3 votes

2 answers

4k views

Prove that a self adjoint and idempotent matrix is a orthogonal projection matrix.

asked Dec 26, 2017 at 15:33

3 votes

3 answers

2k views

Why I can't find modern books on conic sections and analytical geometry?

asked Jun 10, 2017 at 17:29

3 votes

1 answer

520 views

Determinant of sum of squares of two matrices.

asked Aug 16, 2017 at 10:57

3 votes

2 answers

3k views

Surface element of inverted cone in cylindrical coordinates.

asked Jul 11, 2017 at 0:00

3 votes

1 answer

86 views

If $\sum\limits^n_{r=1} r f(r) = n(n+1)$ and $f(1)= \dfrac12$, find $f(1000)$.

asked Sep 9, 2017 at 19:59

2 votes

4 answers

6k views

Isosceles triangle inscribed in an ellipse.

asked Aug 11, 2017 at 20:27

2 votes

1 answer

4k views

Coordinate free equation for electric field by a pure dipole.

asked Aug 12, 2017 at 23:44

2 votes

1 answer

392 views

Method of undetermined coefficients.

asked Jun 24, 2017 at 2:50

2 votes

0 answers

291 views

Counting number of odd permutations using determinants.

asked Nov 9, 2017 at 20:26

2 votes

2 answers

636 views

Can I solve other recurrence relations with linear algebra than just Fibonacci sequence?

asked Dec 17, 2017 at 21:38

2 votes

3 answers

2k views

Uniqueness of minimal norm solution.

asked Dec 23, 2017 at 16:02

2 votes

1 answer

1k views

Prove that if $A \mathbf x = \mathbf 0$ has a unique solution then $A$ is left invertible.

asked Oct 26, 2017 at 16:23

2 votes

2 answers

296 views

Find real and complex $A_{m \times n}$ such that $\operatorname{Ran} A = \operatorname{Ker} A^T$ where $\operatorname{Ran} A$ is column space of $A$.

asked Nov 1, 2017 at 14:40

2 votes

1 answer

1k views

Volume of general parallelepiped.

asked Nov 3, 2017 at 20:47

2 votes

1 answer

3k views

What is the number of multiplications required to find determinant by cofactor expansion?

asked Nov 11, 2017 at 23:50

2 votes

2 answers

392 views

Definition of minor for a general $m \times n$ matrix.

asked Nov 12, 2017 at 14:11

2 votes

0 answers

27 views

Asymptotic analysis of a recurrence relation, $T(n) = \max_{0 \le q \le n-1} (T(q) + T(n - q - 1)) + \Theta(n)$

asked Feb 21, 2020 at 18:00

1 vote

1 answer

111 views

Given that $X,Y,Z$ are independent $U(0, 1)$ distribution, find $\Pr(XY/Z \le t)$.

asked May 17, 2020 at 15:50

1 vote

2 answers

82 views

Eigenvalues and eigenvectors.

asked Dec 12, 2017 at 16:00

1 vote

1 answer

92 views

How to make this argument more rigorous?

asked Nov 17, 2017 at 9:54

1 vote

2 answers

308 views

Is my proof for this linear algebra question correct?

asked Dec 23, 2017 at 22:17

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63 Questions

Good books on complex numbers

Find $\lim\limits_{n \to \infty} \frac{\sqrt 1 + \sqrt 2 + \dots + \sqrt{n}}{n\sqrt{n}}$.

When are definite integrals undefined?

Determinant of a companion matrix

Computing determinant without expansion

Why discriminant of a polynomial is so special?

Find $\sum_{k=1}^{2n} k {2n\choose k}^2 (-1)^{k+1}$. [duplicate]

Prove that pivot columns of row reduced form of any matrix forms a basis in column space of that row reduced matrix.

Definition of transitivity.

Prove that a self adjoint and idempotent matrix is a orthogonal projection matrix.

Why I can't find modern books on conic sections and analytical geometry?

Determinant of sum of squares of two matrices.

Surface element of inverted cone in cylindrical coordinates.

If $\sum\limits^n_{r=1} r f(r) = n(n+1)$ and $f(1)= \dfrac12$, find $f(1000)$.

Isosceles triangle inscribed in an ellipse.

Coordinate free equation for electric field by a pure dipole.

Method of undetermined coefficients.

Counting number of odd permutations using determinants.

Can I solve other recurrence relations with linear algebra than just Fibonacci sequence?

Uniqueness of minimal norm solution.

Prove that if $A \mathbf x = \mathbf 0$ has a unique solution then $A$ is left invertible.

Find real and complex $A_{m \times n}$ such that $\operatorname{Ran} A = \operatorname{Ker} A^T$ where $\operatorname{Ran} A$ is column space of $A$.

Volume of general parallelepiped.

What is the number of multiplications required to find determinant by cofactor expansion?

Definition of minor for a general $m \times n$ matrix.

Asymptotic analysis of a recurrence relation, $T(n) = \max_{0 \le q \le n-1} (T(q) + T(n - q - 1)) + \Theta(n)$

Given that $X,Y,Z$ are independent $U(0, 1)$ distribution, find $\Pr(XY/Z \le t)$.

Eigenvalues and eigenvectors.

How to make this argument more rigorous?

Is my proof for this linear algebra question correct?