Linear algebra.Kernel of a linear mapping

Thread starter manuel325
Start date Jul 10, 2013
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Linear Mapping

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The discussion focuses on finding a basis for the kernel of the linear operator L defined by L(A) = Tr(A), where Tr(A) is the trace of a square matrix A. Participants emphasize the importance of understanding the definition of the kernel, specifically identifying matrices A for which L(A) equals zero. The kernel consists of all matrices whose trace is zero, leading to a deeper exploration of the properties of such matrices. The conversation highlights the need for clarity on the conditions that define the kernel in the context of linear mappings. Understanding these concepts is crucial for solving the problem effectively.

Jul 10, 2013

manuel325

Let ##L## be a linear operator ::##L(A)= Tr(A)## where ##Tr(A)## is the trace of a square matrix
Find a basis of the kernel of L.
Any help would be really appreciated . thanks in advance

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Jul 10, 2013

CompuChip

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How about we start with the definition?
If A is an nxn matrix, what does it mean for A to be in ker L?

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