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Items in Algebra
2. AlgebraIn mathematics, a function
f
{\displaystyle f}
defined on some set
X
{\displaystyle X}
with real or complex values is called bounded if the set of its values (its image) is bounded. In other words, there exists a real number
M
{\displaystyle M}
such that
|
f
(
x
)
|
≤
M
{\displaystyle |f(x)|\leq M}
for all
x
{\displaystyle x}
in
X
{\displaystyle X}
. A function that is not bounded is said to be unbounded.
If
f
{\displaystyle f}
is real-valued and
f
(
x
)
≤
A
{\displaystyle f(x)\leq A}
for all... from wikipedia.org
English:
Assamese:
3. AlgebraIn elementary algebra, a trinomial is a polynomial consisting of three terms or monomials.
== Examples of trinomial expressions ==
3
x
+
5
y
+
8
z
{\displaystyle 3x+5y+8z}
with
x
,
y
,
z
{\displaystyle x,y,z}
variables
3
t
+
9
s
2
+
3
y
3
{\displaystyle 3t+9s^{2}+3y^{3}}
with
t
,
s
,
y
{\displaystyle t,s,y}
variables
3
t
s
+
9
t
+
5
s
{\displaystyle 3ts+9t+5s}
with
t
,
s
{\displaystyle... from wikipedia.org
4. AlgebraIn geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.
== Scalar triple product ==
The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two.
=== Geometric interpretation ===
Geometrically, the scalar triple product
a
⋅
(
b
×
c
)
{\displaystyle \mathbf {a} \cdot (\mathbf {b} \times \mathbf {c} )}
is the (signed) volume of the parallelepiped defined by the three vectors given.
=== Properties ===
The scalar triple product is unchanged under a circular shift of its three operands (a, b, c):... from wikipedia.org