- #1
vish_maths
- 61
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Hello everyone , So here is this problem which i was recently thinking about
Expressing any matrix as the sum of two non singular matrices
So, when i think of ways to express a matrix as sum of two matrices, the thought which
comes first is :
(a) Any matrix can be expressed as the sum of a symmetric and an asymmetric matrix
but an asymmetric matrix is always singular which means this option is ruled out
(b) Suppose A and B are two non Singular matrices. There ought to be some technique
of factorising A and B so that some common terms exist and when i combine these two, a term is obtained whose property defines whether the resulting matrix is singular or not
What can be such a factorisation ?
Expressing any matrix as the sum of two non singular matrices
So, when i think of ways to express a matrix as sum of two matrices, the thought which
comes first is :
(a) Any matrix can be expressed as the sum of a symmetric and an asymmetric matrix
but an asymmetric matrix is always singular which means this option is ruled out
(b) Suppose A and B are two non Singular matrices. There ought to be some technique
of factorising A and B so that some common terms exist and when i combine these two, a term is obtained whose property defines whether the resulting matrix is singular or not
What can be such a factorisation ?
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