5. What is the dimension of n × n-matrices having trace equal to zero as a subspace of Mn × n(𝔽)

Name: 5. What is the dimension of n × n-matrices having trace equal to zero as a subspace of Mn × n(𝔽)?
Uploaded: 2021-12-21T19:34:13-08:00
Duration: 1 min 55 s
Channel: Ben Blakesley
Description: 5. What is the dimension of n × n-matrices having trace equal to zero as a subspace of Mn × n(𝔽)?

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5. What is the dimension of $n \times n$-matrices having trace equal to zero as a subspace of $M_{n \times n}(\mathbb{F})$?

          5. What is the dimension of $n \times n$-matrices having trace equal to zero as a subspace of $M_{n \times n}(\mathbb{F})$?

5. What is the dimension of n × n-matrices having trace equal to zero as a subspace of Mn × n(𝔽)?

Added by Michael R.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

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Solved by Expert Ben Blakesley

12/21/2021

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Step 1: The trace of a matrix is the sum of its diagonal elements. Show more…

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5. What is the dimension of $n \times n$-matrices having trace equal to zero as a subspace of $M_{n \times n}(F)$?

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5. What is the dimension of $n \times n$-matrices having trace equal to zero as a subspace of $M_{n \times n}(\mathbb{F})$?

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