Question

Is set of all orthogonal matrices is a subspace of all matrices?

Answer 1

Answer:

Subspaces of Symmetric, Skew-Symmetric Matrices Let V be the vector space over R consisting of all n×n real matrices for some fixed integer n. Prove or disprove that the following subsets of V are subspaces of V. ... Show that if A is diagonalizable by an orthogonal matrix, then A is a symmetric matrix.

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Answer 2

Answer:

Subspaces of Symmetric, Skew-Symmetric Matrices Let V be the vector space over R consisting of all n×n real matrices for some fixed integer n. Prove or disprove that the following subsets of V are subspaces of V. ... Show that if A is diagonalizable by an orthogonal matrix, then A is a symmetric matrix.

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