What is the difference between matrix dot product and cross product? What is the difference between

The dot product is the inner product of the vector.

The cross product is the outer product of the vector, e.g. dot multiplication: The result of the dot product is a real number.

a·b=|a|·|b|Cosa,b represents the angle between a and b.

Fork Product: The result of a fork product is a vector.

When vectors a and b are not parallel.

The size of the mold is.

a×b|=|a|·|b|The sin is actually the area of the parallelogram constituted by ab).

The direction is. A b and a, b are both vertical.

And a, b, a b into the right hand system.

When a and b are parallel, the result is a vector of 0.

Point multiplication, some software-defined, has nothing to do with matrices, and is the multiplication of corresponding elements.

Cross product, defined in the matrix.

The result of the dot product is a generation, while the result of the cross product is a vector, and its modulo is |a×b|=|a|×|b|×sin(a,b)

Point multiplication is the product of quantities, denoted as a·b; where a·b = a · b cos, a and b are the modulus of the two vectors, which are the angles between the two vectors (0 above a and b are vectors.

The fork product is the product of vectors, denoted as a b, a b = a · b sin, where a and b are the modulus of the two vectors, is the angle between the two vectors (0 above a and b are vectors.

Point multiplicationis the inner product of the vectorFork multiplicationis the outer product of the vector.

Point lead per acre segment multiplication, also called quantity product. The result is the length of one vector projected in the direction of another vector, which is a scalar quantity.

Cross product, also called vector product.

The result is a vector that is perpendicular to both vectors.

Point product. In mathematics, it is also known as the product of quantities (dot product; scalar product) is a binary operation that takes two vectors on a real number r and returns a real scalar. It is the standard inner product of the Euclidean acacia space.

Two vectors a = a1, a2 ,..., an] and b = b1, b2,..., bn] is defined as:

a·b=a1b1+a2b2+……anbn。

Use matrix multiplication.

And the (columnar) vector is treated as an n 1 matrix, and the dot product can also be written as:

a·b = (a t)*b, where a t indicates the transpose of matrix a.

1. The meaning is different:

The dot product is the inner product of the vector.

The cross product is the outer product of the vector.

2. The result units are different:

Point multiplication, which results in the length of one vector projected in the direction of another vector, is a scalar quantity.

Cross product, also called vector product.

As a result, the air is a vector that is perpendicular to both vectors.

3. The calculation method is different:

Point multiplication, formula: a * b = a| *b|*cos cross product, formula: a b = a| *b| *sinθ<>

Point product, also known as the inner product of a vector or quantity product, is the product of the length of a directional family quantity and its projection on another vector.

This definition is only for 2D and 3D space.

Effective. This operation can be simply understood as:

in the dot product. In operations, the first vector is projected onto the second vector (here, the order of the vectors is unimportant, the dot product operation is commutative) and then "normalized" by dividing by their scalar length. Pure disadvantage.

In this way, the score must be less than or equal to 1, which can be simply converted into an angle value.

The geometric meaning of fork multiplication and its application.

Cross product. length of |a×b|It can be interpreted as the area of the parallelogram formed by the two cross-product vectors a and b at the same starting point.

According to this, there is: mixed volume.

abc]=(a b)·c can give a parallelepiped with a, b, c as edges.

volume.

Difference: The dot product is the inner product of the vector and the fork product is the outer product of the vector.

Point Multiplication: The result of the point product is a real number a·b=|a|·|b|Cos cross product: The result of the cross product is a vector.

1. The results of the two operations are different:

1. The result of the operation of dot multiplication: the result obtained is a scalar quantity.

2. The result of the cross product is a vector instead of a scalar.

Second, the scope of application of the two is different:

1. Application range of point multiplication: linear algebra.

2. The application range of fork multiplication: its application is also very wide, usually used in physics optics and computer graphics.

Point product of the vector: a*b.

Formula: a*b=|a|*|b|*cosθ。

Point multiplication, also known as the inner product and quantity product of a vector, is the product of the length of one vector and its projection on another vector; is a scalar quantity.

The dot product reflects the "similarity" of the two vectors, and the more "similar" the two vectors, the greater their dot multiplication.

Cross product of the vector: a b.

a∧b=|a|*|b|*sinθ。

The vector product is defined as:

Modulus length: (here denotes the angle between the two vectors (on the premise of a common starting point) (0° 180°), which is located on the plane defined by the two vectors. ）

Direction: The direction of the vector product of vectors A and B is perpendicular to the plane in which these two vectors are located, and obeys the right-hand rule. (A simple way to determine the direction of a result vector satisfying the "right-hand rule" is this:.)

If the coordinate system satisfies the right-hand rule, when the four fingers of the right hand turn from A to B at an angle of no more than 180 degrees, the thumbs up will point in the direction of C.

For example, multiplication ab

1. 1. Multiply the numbers in the first row of a and the numbers in the first column of b to add them up, which is the number in the first column of the first row in the multiplication result.

2. Multiply the numbers in the first row of a and the numbers in the second column of b to add them up, which is the number in the second column of the first row in the multiplication result.

3) Multiply the numbers in the first row of a and the numbers in the third column of b to add them up, which is the number in the third column of the first row in the multiplication result; This is done in sequence until the numbers in the first row of a are multiplied by the numbers in the last column of b and added up, which is the number in the last column of the first row in the multiplication result.

2. 1. Multiply the numbers in the second row of a and the numbers in the first column of b to add them up, which is the number in the first column of the second row in the multiplication result.

2. Multiply the numbers in the second row of a and the numbers in the second column of b to add them up, which is the number in the second column of the second row in the multiplication result.

3. Multiply the numbers in the second row of a and the numbers in the third column of b to add them up, which is the number in the third column of the second row in the multiplication result; This is done sequentially, (until) the numbers in the second row of a are multiplied by the numbers in the last column of b, and then added up, which is the number in the last column of the second row in the multiplication result, and so on.

Until) multiplies the numbers in the last row of a by the numbers in the first column of b and adds them up, which is the number in the first column of the last row of the multiplication result.

2. Multiply the numbers in the last row of a and the numbers in the second column of b to add them up, which is the number in the second column of the last row in the multiplication result.

3. Multiply the numbers in the last row of a and the numbers in the third column of b to add them up, which is the number in the third column of the last row in the multiplication result; This is done sequentially, (until) the numbers in the last row of a are multiplied by the numbers in the last column of b and added up, which is the number in the last row and the last column of the multiplication result.

Tips for learning math.

1. Be good at thinking when learning mathematics, and the answers you come up with are far more impressive than the answers told by others.

2. Do a good job of preview before class, and take turns so that you can better digest and absorb the knowledge points that you don't know when you take math classes.

3. Mathematical formulas.

It must be memorized, and the fiber book must also be able to deduce, and be able to draw inferences.

4. The most basic thing to learn mathematics well is to master the knowledge points of the textbook and the exercises after class.

5. 80% of the scores in mathematics are in the basic knowledge, and 20% of the scores are difficult, so it is not difficult to score 120 points. Brother Lazhu.

The dot multiplication yields a numerical value: the product of the two vector modulus multiplied by the cos of their angles

The cross multiplication gives a vector: the magnitude is the product of the two vector modulus multiplied by the sin of their angles, and the direction is perpendicular to both vectors.

Difference: Blind mindfulness of multiplication.

is the inner product of the vector, the cross product.

is the outer product of the vector.

1. Point product: also called the product of quantities, the result is the length of one vector projected in the direction of another vector, which is a scalar quantity.

2. Fork multiplication: It is also called the vector product.

The result is a vector that is perpendicular to both vectors.

In terms of graphics, the general point grinding multiplication is used to determine whether two vectors are perpendicular or not, and can be used to calculate the projection length of a vector in a certain direction, just like the definition. The cross product is more to judge the direction of a certain plane, and select two non-collinear vectors from this plane, and the result of the cross product is the normal vector of this plane.