MindMap Gallery Quadratic type
This is a mind map about the quadratic form of advanced algebra. The quadratic form is a polynomial in which there are any number of unknowns, but the degree of each term is 2.
Edited at 2024-03-07 22:40:34This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
Quadratic type
Study its simplification
Matrix representation
Introducing contract transformations in matrices
concept
nature
judge
Use contract transformation to transform into a diagonal matrix
The inverse is a binomial
polynomial representation
Introducing non-degenerate linear substitution
judge
use
Use the recipe
Each recipe will be one less
Classification
Zhengding
concept
Determination (nature of use)
Positive inertia is n (n-dimensional quadratic type)
The standard coefficients are all positive numbers (n) or the matrix can be transformed into a diagonal matrix and all elements on the diagonal are >0
Sequential main subexpression>0
The matrix can be reduced to the identity matrix
necessary conditions
Elements on the diagonal of the matrix > 0
Matrix corresponding determinant>0
negative definite
concept
Judgment (imitating Zhengding, the latter is special)
Even order sequence principal formula>0
Odd-order sequential principal formula<0
Necessary conditions (column special)
The corresponding determinant of the matrix is not necessarily <0
semi-positive definite
concept
nature
Positive inertia is r (r<n), negative inertia is 0
Sequential principal expression ≥ 0
semi-negative definite
concept
Properties (imitating positive semi-definite)
indefinite
concept
Nature (judgment)
There is no good method, just rely on concepts, it is not difficult to practice
judgment contract
inertia theorem
Standard type is not unique
Utilize non-degenerate linear substitution
Canonical form (unique)
Each coefficient is one or negative one
Standard type
will become a quadratic form with only square terms
Utilize non-degenerate linear substitution