Positive Definite Matrices Explanation,Tests, CSIR NET previous years questions solved

Positive Definite Matrices Explanation,Tests, CSIR NET previous years questions solved. Useful for CSIR NET, GATE, UPSC and other competitive Examination.
Completing the square or energy test for positive definite, Sylvester's criteria or determinant rule for positive deifinte, eigenvalue tests for positive definite matrix or Pivot test( or converting into echelon form ) for positive definite matrix

Link to positive definite matrices based solved problems:

[avanishmishra]

You explained everything very easily very nice explanation

[AbhishekKashyap-kkqv]

Mam In the last question I think option d i.e Q<0 is not correct .if it is correct then all the eigen values should be negative but there are two positive eigen values so I think it's correct ans should be only A.

[rajatsharma-xbdk]

very much concrete and to the point with examples, well done mam.

[MaheshKumar-ybkn]

when we use determinant method for finding positve definite matrix, is there any condition of given matrix should be symmetric ? because you have taken the example matrix is 4 5 6 and 7 8 9 and 10 11 12 problem, this matrix is actually not a symmetric

[sahilarora]

Hi, can u make video schlur lemma in linear algebra ?

[SUNILSINGH-rhlv]

Mam plz tell best books for csir net math

[kuldeepnet]

Madam multplication of matrices in first example is wrong