"Vector"-Schematic linear algebra 01

This paper turns from the public number---meets the mathematical---graphic mathematical---linear algebra part

Thank you for meeting the Math Working Group to explain the obscure and acting knowledgeable mathematical knowledge of university textbooks in an easy-to-understand and lively and interesting way.

The concept of vectors

In real life, we put a few values together, as a whole to analyze, and this has vector (vectors)? an ordered list of values.

To separate the vectors from the dots, it is customary to write the logarithm vertically and enclose it in parentheses, such as the following example, 2-dimensional vector, 3-dimensional vector, and 4-dimensional vector:

Note: or use square brackets

Deciding on a vector is its length and direction, and we can understand it better through a coordinate system. The arrows are drawn in a two-dimensional coordinate system, and the starting point of the arrow is at the origin, and the end point is the one corresponding to the value component. Thus each vector corresponds to a unique logarithm, and a pair of numbers in the coordinate system uniquely corresponds to a vector.

As long as the vectors are the same size and direction, they are considered equal vectors, as shown in the two-dimensional plane (two-dimensional), randomly moving a vector, leaving the trajectory is the same vector:

and the vector of the three-dimensional space will have three components, we use the z-axis to express, so that each vector will also correspond to an ordered ternary array:

Addition of vectors

Vector addition is the addition of the corresponding items:

From the graph we can translate the second vector so that its starting point coincides with the end point of the first vector, and then draw a vector that starts from the beginning of the first vector and points to the end of the second vector. This vector is their and; Or observing that the animation is moving according to the component of each vector the final effect is the same:

The multiplication of vectors

Another basic vector operation is a numeric value (scalar scalar) multiplied by each component of the vector, which multiplies each component in the vector by a scalar. If you choose a value of 2, multiply it with a given direction, which means that you lengthen the vector to twice times the original vector:

Observe if the scalar is negative, the result vector is reversed. That is, the multiplication vector is actually the stretching, compressing, or reversing of the vector:

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The addition and multiplication of vectors is very important and will run through linear algebra, so we'll end up with the first one, but add a few more diagrams below to deepen the understanding of addition:

The vector addition triangle rule is actually the same as the above addition, but the vector starting point here is not the origin:

Vector addition Polygon rule:

Parallelogram principle

The subtraction of vectors is actually a special case of addition:

"Vector"-Schematic linear algebra 01