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Curl of a Vector Field
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Divergence of a Vector Field
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Gradient of a Scalar Field
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Properties of Transposes
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The Transpose of a Matrix
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Cartesian Coordinate
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Cylindrical Coordinate
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Spherical Coordinate
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Transform from Cartesian to Cylindrical Coordinate
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Transform from Cartesian to Spherical Coordinate
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Transform from Spherical to Cartesian Coordinate
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Divergence Theorem/Gauss' Theorem
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Stokes' Theorem
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Definition of a Matrix
Current Location
>
Math Formulas
>
Linear Algebra
> Definition of Zero Matrix
Definition of Zero Matrix
A matrix is known as a
zero
or
null matrix
if all of its elements are zero.
Examples:
etc. are all zero matrices.
If you add the
m
×
n
zero matrix to another
m
×
n
matrix A, you get A:
In symbols, if 0 is a zero matrix and A is a matrix of the same size, then
A
+ 0 =
A
and 0 +
A
=
A
A zero matrix is said to be an
identity element
for matrix addition. A zero matrix serves many of the same functions in matrix arithmetic that 0 does in regular arithmetic.
Example 1:
What is the resultant when we add the given matrix to the null matrix?
Solution:
We know that
A
+ 0 =
A
Therefore,
Example 2:
Show that the sum of matrix Q and its additive inverse is a zero matrix.
Solution:
Its additive inverse is given by
Now
Hence the sum of matrix Q and its additive inverse is a zero matrix.
Example 3:
What is the resultant when we add the given matrix
A
to the null matrix?
Solution:
We know that
A
+
0
=
A
Therefore,
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