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Exercise 21

Avg difficulty 3.0

A square matrix is symmetric if for all indices ii and jj, entry i,ji,j equals entry j,ij,i.

  • Find a basis for the vector space of symmetric 2 ⁣× ⁣22\!\times\!2 matrices.

  • Find a basis for the space of symmetric 3 ⁣× ⁣33\!\times\!3 matrices.

  • Find a basis for the space of symmetric n ⁣× ⁣nn\!\times\!n matrices.

Hefferon, Linear Algebra, Vector Spaces, Basis, Exercise 21

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.