Newbetuts

Prove that the distance between parallel planes $\vec{n}\cdot \vec{x} = d_1 $, $\vec{n}\cdot \vec{x}=d_2$ is $|d1-d2|/||\vec{n}||$

Positive semidefiniteness of a block matrix of positive semidefinite matrices

What should we understand from the definition of orthogonality in inner product spaces other than $\mathbb R^n$?

example of a nonempty subset is closed under scalar multiplication but not a subspace

Regarding trace of idempotent matrix multiplied by its transpose

Connection between linear independence, non-/trivial and x solutions

The tangent space of a manifold at a point given as the kernel of the jacobian of a submersion

If $A \in M_{n,n}(\mathbb F)$ is invertible then $A = UPB$, $U$ is unipotent upper triangular, $B$ is upper triangular and $P$ is a permutation.

Geometric meaning of a matrix decomposed into its symmetric and skew-symmetric parts

Number of Jordan forms from given characteristic polynomial and partitions

A polynomial that annihilates two other

For $T\in \mathcal L(V)$, we have $\text{adj}(T)T=(\det T)I$.

Connection between rank and positive definiteness

Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular

Proof of "every finite dimensional vector space has a finite basis"

The number of esquares of idempotents in the rank 2 $\mathcal{D}$-class of $M_n(\mathbb{Z}_2)$.

Is the function T $\mathbb R$-linear?

New posts in linear-algebra

Proof that Every Positive Operator on V has a Unique Positive Square Root

diagonalizing a matrix over the $\ell$-adics

Farkas Lemma proof

Prove that the distance between parallel planes $\vec{n}\cdot \vec{x} = d_1 $, $\vec{n}\cdot \vec{x}=d_2$ is $|d1-d2|/||\vec{n}||$

Positive semidefiniteness of a block matrix of positive semidefinite matrices

What should we understand from the definition of orthogonality in inner product spaces other than $\mathbb R^n$?

example of a nonempty subset is closed under scalar multiplication but not a subspace

Regarding trace of idempotent matrix multiplied by its transpose

Connection between linear independence, non-/trivial and x solutions

The tangent space of a manifold at a point given as the kernel of the jacobian of a submersion

If $A \in M_{n,n}(\mathbb F)$ is invertible then $A = UPB$, $U$ is unipotent upper triangular, $B$ is upper triangular and $P$ is a permutation.

Geometric meaning of a matrix decomposed into its symmetric and skew-symmetric parts

Number of Jordan forms from given characteristic polynomial and partitions

A polynomial that annihilates two other

For $T\in \mathcal L(V)$, we have $\text{adj}(T)T=(\det T)I$.

Connection between rank and positive definiteness

Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular

Proof of "every finite dimensional vector space has a finite basis"

The number of esquares of idempotents in the rank 2 $\mathcal{D}$-class of $M_n(\mathbb{Z}_2)$.

Is the function T $\mathbb R$-linear?