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Can $A^3=0$ imply $|I+A|=0$?

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#linear-algebra #matrices #determinant
251
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Any two complex square matrices are triangulable in the same basis, albeit perhaps in different orders

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#linear-algebra #matrices #vector-spaces #eigenvalues-eigenvectors
2k
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What is the geometric intuition behind algebraic multiplicity?

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#linear-algebra #linear-transformations
60
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Let $P,P' $ be proper subspaces of finite dimension vector space $V$ $\Rightarrow$ $\exists$ $S$ , such that $V = S \bigoplus P = S \bigoplus P'$

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#linear-algebra
108
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Easier way to identify a 3 variable determinant as symmetric polynomial

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#linear-algebra #matrices #determinant #symmetric-polynomials
237
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Learning a point on the sphere using signs of dot products

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#linear-algebra #geometry #spherical-geometry #geometric-probability
56
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Proving vectors are rotations about some axis

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#linear-algebra
1.6k
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If every linear functional on the vector space $V$ is continuous, then $V$ has finite dimension

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#linear-algebra #functional-analysis #vector-spaces
152
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Find the base of the kernel of $L(y)=x^2y''-3xy'+3y.$

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#linear-algebra #ordinary-differential-equations
384
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Finding Jordan-normal form of a special $n\times n$ matrix

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#linear-algebra #ordinary-differential-equations #jordan-normal-form
3.7k
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Operator norm and unitary matrix

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#linear-algebra #matrices #functional-analysis #unitary-matrices
53
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Determining if a linear equation system only has a specific solution given a condition.

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#linear-algebra #systems-of-equations
2.4k
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How do I determine whether the orientation of a basis is positive or negative using the cross product

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#linear-algebra #vector-spaces #orthonormal #orientation
969
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About definition in Linear Algebra concerning empty subset of vector space

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#linear-algebra #definition
54
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Eigenvalues for an expression

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#linear-algebra #matrices #eigenvalues-eigenvectors #determinant

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