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Linear Independence - Vectors in $\Bbb{R}^4$

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#linear-algebra
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Prove if $\lambda$ is eigenvalue of X, then $\lambda$ is an eigenvalue of $X^T$

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#linear-algebra
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how do we find the nature of lines represented by a system of linear equations?

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#linear-algebra #geometry #systems-of-equations #3d #coordinate-systems
474
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Determining whether a set of vectors spans $\mathbb{R^n}$

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#linear-algebra #determinant
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How to show that linear applications are closed and open

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#linear-algebra #linear-transformations #open-map #closed-map
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what does these signify: $zA^kb=0$

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#linear-algebra #eigenvalues-eigenvectors
337
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Matrix derivation of the normal equations - how to properly differentiate?

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#linear-algebra #matrices #regression
560
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How to find eigenvectors of a nxn matrix

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#linear-algebra #eigenvalues-eigenvectors
52
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Prove that there is an index $j\in J\setminus I$ such that $(I \backslash \{i\})\cup\{j\}$ is a basis and so is $(J \setminus \{j\})\cup \{I\}$

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#linear-algebra #proof-writing
350
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Possible Jordan Normal Forms

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#linear-algebra #jordan-normal-form #minimal-polynomials
122
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How to construct the isomorphism between two 3-dimensional simple Lie algebras over C?

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#linear-algebra #representation-theory #lie-algebras
74
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Linear Algebra, matrix for a linear transformation

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#linear-algebra #linear-transformations
78
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Subspace in C[0,1]

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#linear-algebra
201
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Strong Basis Exchange in Linear Algebra

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#linear-algebra #vector-spaces
643
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The linear operator $T_A(B)=AB-BA$ defined on $\mathbb M_n(\mathbb C)$ has a null determinant

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#linear-algebra #matrices #proof-verification #determinant

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