Lec - 21 Nilpotent Matrix | Properties of Nilpotent matrix | IIT JAM | CSIR UGC NET | TIFR | DU

NOTE: Something was missing in the Result (3) which is diagonal entries are Non-zero with the same sign (All non-zero entries of diagonal are positive or all non-zero entries of diagonal are negative). Special Thanks for @Purvi who caught the error.

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#indexofnilpotent

[MathematicalScience]

NOTE: Something was missing in Result (3) which is applied only for upper or lower triangular nilpotent matrix.

[sudiptasarkar]

If first row 1, -1, 1
2nd row -3, 3, -3
3rd row - 4, 4, -4
Then A^2=0
So nikpotent
All elements in principle diagonal line are non zero
Sir plz ans boliye

[aakashlone]

Sir plx continue ..ring theory ....plx ..but fast

[purvidesai]

sir for note (3), let [A] 3*3 = [ (1, 1, 3 ) (5, 2, 6) (-2, -1, -3) ] has non zero diagonal element , Still A^3 = 0, i.e. nilpotent
something missing ?
thank you

[sangam]

How to find the rank of nilpotent matrix of order n?

[subhajitbera]

Sir please upload ring theory next lecture

[vidhiyadav]

sir in one of the properties you mentioned that AB is nilpotent ifAB=BA... last qsn mein given tha AB is nilpotent to mtlb AB=BA hai to mtlb AB=BA ek matrix h to agar AB nilpotent hai to kya hum direct ni bol slte BA bhi hoga as it is equal to AB

[aakashlone]

If you want to help poor student like me then sir upload plx fast vedios of ring theory ....and your choice I, e linear algebra....plx go fast, ,exams are near by

[babitarawat]

Sir i didn't understand the inequality used for index why we have used less than equal sign
Index is least no. To make the matrix zero so the inequality should be greater than equal right?
Please clear my doubts

[akshaydarji]

Let A be 2×2 matrix such that A^102=0. Then
a) p^2=0
b) ( l - A) ^2 = 0
c) ( I + A) ^2 =0
d) A = 0
Please sir Help me