Newbetuts

Let $U,\ W \leq V$ subspaces of a vector space V. What could the dimension of $U \cap W$ be, if $\dim{U} = 4,\ \dim{W} = 5,\ \dim{V} = 7$?

Let $A\in M_n(\Bbb R)$ prove that, $\|A^n\|\le \frac{n}{\ln 2}\|A\|^{n-1}$ when $\lambda_i<1.$

Is the function $A \mapsto \sum\limits_{j=0}^{\infty} \langle A^j v, A^j v \rangle$ differentiable everywhere?

Prove that matrices of this form have eigenvalues $0,1,\ldots , n-1$

Is there a geometric proof that the determinant of a 3x3 matrix is invariant under switching rows and columns?

Linear algebra and arbitrary fields

Matrix factorization

Showing that $x^{\top}Ax$ is maximized at $\max \lambda(A)$ for symmetric $A$

When pseudo inverse and general inverse of a invertible square matrix will be equal or not equal?

proof of basic fact that torus actions are diagonalizable

Is the rank of the sum of two positive semi-definite matrices larger than their individual ranks?

find all the values of a and b so that the system has a) no solution b) 1 solution c) exactly 3 solutions and 4) infinitely many solutions

Is it true that the whole space is the direct sum of a subspace and its orthogonal space?

inverse of diagonal plus sum of rank one matrices

How many ways are there to prove Cayley-Hamilton Theorem?

Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$

New posts in linear-algebra

Aluffi's proof that $\det(AB)=\det(A)\det(B)$ for commutative rings

The question about the vector space

How does Cholupdate work?

Trying to determine the determinant of an abstract matrix

Let $U,\ W \leq V$ subspaces of a vector space V. What could the dimension of $U \cap W$ be, if $\dim{U} = 4,\ \dim{W} = 5,\ \dim{V} = 7$?

Let $A\in M_n(\Bbb R)$ prove that, $\|A^n\|\le \frac{n}{\ln 2}\|A\|^{n-1}$ when $\lambda_i<1.$

Is the function $A \mapsto \sum\limits_{j=0}^{\infty} \langle A^j v, A^j v \rangle$ differentiable everywhere?

Prove that matrices of this form have eigenvalues $0,1,\ldots , n-1$

Is there a geometric proof that the determinant of a 3x3 matrix is invariant under switching rows and columns?

Linear algebra and arbitrary fields

Matrix factorization

Showing that $x^{\top}Ax$ is maximized at $\max \lambda(A)$ for symmetric $A$

When pseudo inverse and general inverse of a invertible square matrix will be equal or not equal?

proof of basic fact that torus actions are diagonalizable

Is the rank of the sum of two positive semi-definite matrices larger than their individual ranks?

find all the values of a and b so that the system has a) no solution b) 1 solution c) exactly 3 solutions and 4) infinitely many solutions

Is it true that the whole space is the direct sum of a subspace and its orthogonal space?

inverse of diagonal plus sum of rank one matrices

How many ways are there to prove Cayley-Hamilton Theorem?

Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$