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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Sourav Ghosh posted an Question
April 05, 2020 • 02:54 am
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10 points
10 points
- CSIR NET
- Mathematical Sciences
Zero Eigen Vector
why X= zero vector is not accepted as a eigen vector.It is always a member of the nullspace of every matrix.
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Priyadarshan Choursiya Best Answer
main reason is in definition. see attachment
b :eigen value of A,then (A-bI)X=0 and whatever the value of b maybe ,the nullspace of the matrix(A-bI) always contain ZERO vector.And we dont accept ZERO vector as a eiven vector corresponding to b.Sorry for calling eigen value b.
but sir, definition says that you never take x = 0 eigen vector, so we can't make any change in it. we have to accept the definition as it. this the main reason of your question, other results are just derived from them
0 always belongs to null space. here we are finding non zero elements in null space of corresponding matrix
even zero matrix has non zero eigen vectors.
THANKS SIR.