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Example Question #5 : Symmetric Matrices
Example Question #6 : Symmetric Matrices
Example Question #7 : Symmetric Matrices
Example Question #8 : Symmetric Matrices
Example Question #11 : Symmetric Matrices
Example Question #12 : Symmetric Matrices
Example Question #11 : Symmetric Matrices
Example Question #12 : Symmetric Matrices
True or false: is an example of a skew-symmetric matrix.
True
False
False
A square matrix is defined to be skew-symmetric if its transpose
- the matrix resulting from interchanging its rows and its columns - is equal to its additive inverse; that is, if
.
Interchanging rows and columns, we see that if
,
then
.
can be determined by changing each element in
to its additive inverse:
, since not every element in corresponding positions is equal; in particular, the three elements in the main diagonal differ.
is not a skew-symmetric matrix.
Example Question #71 : Operations And Properties
True or false: is an example of a skew-symmetric matrix.
True
False
True
A square matrix is defined to be skew-symmetric if its transpose
- the matrix resulting from interchanging its rows and its columns - is equal to its additive inverse; that is, if
.
Interchanging rows and columns, we see that if
,
then
.
We see that each element of is the additive inverse of the corresponding element in
, so
, and
is skew-symmetric.
Example Question #153 : Linear Algebra
is a three-by-three nonsingular skew-symmetric matrix
Then which of the following must be equal to ?
A square matrix is defined to be skew-symmetric if its transpose
- the matrix resulting from interchanging its rows and its columns - is equal to its additive inverse; that is, if
.
Therefore, by substitution,
must be equal to the opposite of the three-by-three identity matrix, which is
.
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