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Ben McKay
Ben McKay
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problems Problems concerning subspacesubspaces of M_n$M_n(\mathbb{C})$

let M_n(c)Let $M_n(\mathbb{C})$ denote the n times n matrices over the complex number field. N be a subspace of

M_n(C) $M_n(\mathbb{C})$.

  1. ifIf all the matrices in N are non-invertible , what is the maximum of the dimension of N can be?

  2. ifIf all the matrices in N commute with each other  , what is the maximum of the dimension of N can be?

  3. ifIf all the matrices in N are nilpotent  , what is the maximum of the dimension of N can be?

  4. ifIf all the non-zero matrices in N are invertible  , what is the maximum of the dimension of N can be?

problems concerning subspace of M_n(C)

let M_n(c) denote the n times n matrices over the complex number field. N be a subspace of

M_n(C).

  1. if all the matrices in N are non-invertible , what is the maximum of the dimension of N can be?

  2. if all the matrices in N commute with each other  , what is the maximum of the dimension of N can be?

  3. if all the matrices in N are nilpotent  , what is the maximum of the dimension of N can be?

  4. if all the non-zero matrices in N are invertible  , what is the maximum of the dimension of N can be?

Problems concerning subspaces of $M_n(\mathbb{C})$

Let $M_n(\mathbb{C})$ denote the n times n matrices over the complex number field. N be a subspace of $M_n(\mathbb{C})$.

  1. If all the matrices in N are non-invertible , what is the maximum the dimension of N can be?

  2. If all the matrices in N commute with each other, what is the maximum the dimension of N can be?

  3. If all the matrices in N are nilpotent, what is the maximum the dimension of N can be?

  4. If all the non-zero matrices in N are invertible, what is the maximum the dimension of N can be?

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zhaoliang
zhaoliang
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problems concerning subspace of M_n(C)

let M_n(c) denote the n times n matrices over the complex number field. N be a subspace of

M_n(C).

  1. if all the matrices in N are non-invertible , what is the maximum of the dimension of N can be?

  2. if all the matrices in N commute with each other , what is the maximum of the dimension of N can be?

  3. if all the matrices in N are nilpotent , what is the maximum of the dimension of N can be?

  4. if all the non-zero matrices in N are invertible , what is the maximum of the dimension of N can be?