Question

Suppose A is an m-by-n matrix with $A\ne0$. Prove that the rank of A is 1 if and only if ....

score 860 · Answer 1 · 2020-12-04 12:45:46

860

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Suppose A is an m-by-n matrix with $A\ne0$. Prove that the rank of A is 1 if and only if ....

Published on 04 Dec 2020 - 12:45

score 396 · Answer 2 · 2026-03-28 01:26:00

396

Views

Making a matrix have a certain rank

Published on 28 Mar 2026 - 1:26

score 17 · Answer 3 · 2020-12-05 10:45:44

17

Views

$W$ contains at least one non-singular matrix

Published on 05 Dec 2020 - 10:45

score 29 · Answer 4 · 2020-12-05 11:25:42

29

Views

An example of matrices $A_1$ and $A_2$, for which the rank of sum $A_1+A_2$ is greater than $max(r_1, r_2)$

Published on 05 Dec 2020 - 11:25

score 74 · Answer 5 · 2020-12-05 12:03:37

74

Views

Finding rank of linear transformation from

Published on 05 Dec 2020 - 12:03

score 473 · Answer 6 · 2026-03-27 17:24:27

473

Views

How to show that $A′A$ is a positive deﬁnite matrix given rank$(A) = k$?

Published on 27 Mar 2026 - 17:24

score 62 · Answer 7 · 2020-12-08 11:37:34

62

Views

How does the matrix logarithm change when a matrix is extended with zero rows and columns?

Published on 08 Dec 2020 - 11:37

score 27 · Answer 8 · 2020-12-10 01:50:30

27

Views

The number of solutions to $Ax=b$, is either zero, or if a solution exists, then equal to the size of the null space of $A$

Published on 10 Dec 2020 - 1:50

score 83 · Answer 9 · 2020-12-10 13:03:09

83

Views

Prove that determinant is zero iff $x= 2, 3$

Published on 10 Dec 2020 - 13:03

score 34 · Answer 10 · 2020-12-11 17:52:54

34

Views

Given two solution vectors - finding the general solution

Published on 11 Dec 2020 - 17:52

score 56 · Answer 11 · 2026-03-30 15:30:51

56

Views

If $rank(S) \leq nullity(T)$ then is $rank(S^) \geq nullity(T^)$?

Published on 30 Mar 2026 - 15:30

score 134 · Answer 12 · 2020-12-13 23:03:51

134

Views

matrix interesting problem about determinant

Published on 13 Dec 2020 - 23:03

score 182 · Answer 13 · 2020-12-15 11:37:14

182

Views

Proof/Counterexample: Any two 6x6 matrices are similar of they have the same rank and same minimal polynomial

Published on 15 Dec 2020 - 11:37

score 238 · Answer 14 · 2020-12-15 12:52:42

238

Views

Prove $\operatorname{rank}(A^*A)=\operatorname{rank}(A)$

Published on 15 Dec 2020 - 12:52

score 101 · Answer 15 · 2026-03-26 10:57:59

101

Views

full rank by inspection

Published on 26 Mar 2026 - 10:57

List Question

Suppose A is an m-by-n matrix with $A\ne0$. Prove that the rank of A is 1 if and only if ....

Making a matrix have a certain rank

$W$ contains at least one non-singular matrix

An example of matrices $A_1$ and $A_2$, for which the rank of sum $A_1+A_2$ is greater than $max(r_1, r_2)$

Finding rank of linear transformation from

How to show that $A′A$ is a positive deﬁnite matrix given rank$(A) = k$?

How does the matrix logarithm change when a matrix is extended with zero rows and columns?

The number of solutions to $Ax=b$, is either zero, or if a solution exists, then equal to the size of the null space of $A$

Prove that determinant is zero iff $x= 2, 3$

Given two solution vectors - finding the general solution

If $rank(S) \leq nullity(T)$ then is $rank(S^) \geq nullity(T^)$?

matrix interesting problem about determinant

Proof/Counterexample: Any two 6x6 matrices are similar of they have the same rank and same minimal polynomial

Prove $\operatorname{rank}(A^*A)=\operatorname{rank}(A)$

full rank by inspection

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