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What does n-dimensional vector mean
N-dimensional vector with n coordinate components, i.e. vectors in n-dimensional space
For example, a plane is two-dimensional, equivalent to a two-dimensional vector
For example, a solid is three-dimensional, equivalent to a three-dimensional vector
What does the length of the n-dimensional column vector is 1 mean Given a is n-dimensional column vector and its length is 1, prove matrix H=E-2aa^T
The length of the n-dimensional column vector is 1, meaning a^Ta=1
When m > n, m n-dimensional vectors must be linear (, You'd better write down the process.
Related,
Let An×m=(α1,
α2,...,αM), then R (A)≤n.
Sublinear equations Ax=x1α1+x2α2+...+xmαm=0 have nonzero solutions.m
N-dimensional vector vectors α1,α2,...,αm must be linearly related.
A vector group consisting of m n-dimensional vectors must be linearly related when (). Fill in the blanks A vector group consisting of m n-dimensional vectors is linearly related when (). Fill in the blanks
M > n
M n-dimensional vectors (m > n), linear correlation? , Analyze from row and column vectors
Linear correlation.
If the number of vectors is larger than the dimension of the vector, the vector group is linearly related.
Row vector column vector one thing.
A is the vector of n-dimensional unit column, and A=E-aa^T is the rank of A
The characteristic value of known aa^T is 1,0,0,...,0
Therefore, the characteristic value of A=E-aa^T is 0,1,1,...,1
Since A is a real symmetric matrix, r (A) is equal to the number of nonzero eigenvalues of A, i.e. r (A)= n-1.
RELATED INFORMATIONS
- 1. What is the difference between n-dimensional unit column vector and n-dimensional unit vector
- 2. A is n-dimensional orthogonal matrix, a, b is n-dimensional column vector, then Aa·Ab=a·b. Why?
- 3. Given vector a=(x^2-3,1) b=(x,-y), when x <2 in absolute value, there is a⊥b, when x≥2 in absolute value, a‖b Given vector a=(x^2-3,1) b=(x,-y),(where y and x are not equal to 0), when x <2 in absolute value, there is a⊥b, when x≥2 in absolute value, a‖b, find function y=f (x)
- 4. The vector a=(cosα, sinα), b=(cosβ, sinβ),0<β<α If |a-b|=root2 find a perpendicular b let c=(0,1) if a+b=c find the value of The vector a=(cosα, sinα), b=(cosβ, sinβ),0<β<α If |a-b|=rootoot 2, find a perpendicular b Let c=(0,1) If a+b=c, find the value of
- 5. What is the difference between quantity product and vector product? Why the quantity product is perpendicular if the vector a* vector b=0 and the vector a* vector b=0 if the vector product is parallel What is the area of the quantity product and the vector product? Why is the quantity product vertical if the vector a* vector b=0 and the vector product parallel if the vector a* vector b=0?
- 6. Vector a+b=(-2,-1), a-b=(4,-3), the angle between vector a, b is
- 7. Given that M={ a|a=(2 1,-2-2), R}, N={ b|b=(3 2,6 1), R}, is a set of vectors, then M∩N= Options have four A {c|c (-2,1)} B {c|c (2,1)} C {c|c (-2,1)} D {c|c (2,1)}
- 8. Given that point D is the midpoint of the edge BC of the triangle, there is a point P in the plane where the triangle ABC is located, which satisfies vector PA + vector BP + vector CP =0, The module of vector PA is divided by the module of vector PD is equal to λ, and the value of λ is obtained.
- 9. Given vector a=(1, x), vector b=(x^2+x,-x), m is constant and m≤-2 Given vector a=(1, x), vector b=(x^2+x,-x), m is constant and m≤-2 Let a · b +2> m ((2/(a · b))+1). How did x get? Given vector a=(1, x), vector b=(x^2+x,-x), m is constant and m≤-2 Given vector a=(1, x), vector b=(x^2+x,-x), m is constant and m≤-2 Let a · b +2> m ((2/(a · b))+1). How was x found? Given vector a=(1, x), vector b=(x^2+x,-x), m is constant and m≤-2 Given vector a=(1, x), vector b=(x^2+x,-x), m is constant and m≤-2 Let a·b+2> m ((2/(a·b))+1). How did you get x?
- 10. Given vector OA=(3,-4), vector OB=(6,-3), vector OC=(5-x,-3-y), if A, B, C can form a triangle, find the condition that x, y satisfies.
- 11. Let the sum of the elements of any row of matrix A of order n be a and prove that a is a eigenvalue of matrix A to find the eigenvector corresponding to a Let a be the sum of the elements of any matrix A of order n be a and prove that a is a eigenvalue of matrix A to find the eigenvector corresponding to a
- 12. Vector midpoint proof In the known isosceles triangle ABC,∠C=90°, D is the midpoint of CB, E is the point on AB, and AE=2EB.
- 13. Is a linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, then they are called orthogonal vector sets "orthogonal to any two vectors? Linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, it is called orthogonal vector set "is any two vectors orthogonal? Linear algebra problem," a set of nonzero n-dimensional vectors, if they are orthogonal to each other, then it is called orthogonal vector set "Is any two vectors orthogonal?
- 14. For the vector a, b, c and the real number λ, is the true proposition () in the following propositions possible to analyze these four in detail? A. If a*b=0, then a=0 or b=0 B. If λa=0, then λ=0 or a=0 C. If a^2= b^2, then a = b or a =-b D. If a*b=a*c, then b=c For the vector a, b, c, and real number λ, could the following real proposition () analyze these four in detail? A. If A*B=0, then A=0 or B=0 B. If λa=0, then λ=0 or a=0 C. If A2= B2, then A = B or A = B D. If a*b=a*c, then b=c
- 15. N +1 n-dimensional vector, composed of vector group dimension linear (? ) Vector Group N +1 n-dimensional vector, the vector group composed of linear (? ) Vector Group
- 16. It is proved that in n-dimensional vector space, if α1.α2...αn is linearly independent, then any vector β can be linearly represented by α1.α2..αn. It is proved that any vector β can be linearly represented by α1.α2...α n if α1.α2...
- 17. Let A be the s×m matrix, B be the m×n matrix, and X be the vector of n-dimensional unknown columns. Let A be the s×m matrix, B be the m×n matrix, and X be the vector of n-dimensional unknown columns. AB has the same rank as B, i.e. r (AB)=r (B) Let A be the s×m matrix, B be the m×n matrix, and X be the vector of n-dimensional unknown columns. Let A be the s×m matrix, B be the m×n matrix, and X be the vector of n-dimensional unknown columns. AB has the same rank as B, i.e. r (AB)= r (B)
- 18. Let A be a real matrix of m*n and A^TA be a positive definite matrix. It is proved by data that r (A^TA)≤r (n)≤n, but I don't know where this formula comes from, and the formula is r (AB)≤r (A), r (AB)≤r (B),. I've found the problem in the book, and now there's another question: Shouldn't r (A)≤min {m, n}? Why is the formula directly r (n)≤n? Somebody help me.
- 19. Matrix proof: If the matrix of order n satisfies AA^T=E, it is proved that x^TAx=0. If the matrix of order n satisfies A^T=-A, it is proved that x^TAx=0.
- 20. Let a, b be n-dimensional nonzero column vectors, matrix A=2E (N-dimensional)-abt (transposed vector of b) What is the transposition vector of a multiplied by b if the square of A = A +2E