A linear combination of and can have determinant zero.

Any symmetric matrix can be written as a combination of .

is symmetric.

are linearly independent.

can be expressed as a linear combination of .

is diagonal.

is not symmetric.

Any two of can form a basis of .

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is linearly independent.

can be written as a combination of and .

can be written as a linear combination of and .

is linearly independent.

is always a subspace of .

is always a subspace of .

is always a subspace of .

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If , then .

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The Fourier series converges uniformly to on .

For any closed subinterval that does not contain , the Fourier series converges uniformly to on .

The Fourier series converges to at .

The Fourier series of converges pointwise to for every .

The Fourier series of converges pointwise to for every .

The Fourier series of a function always converges pointwise to .

The Fourier series of a trigonometric polynomial always converges pointwise to .

Two different discontinuous functions might share the same Fourier coefficients.

Fourier series do not converge uniformly near discontinuities.

The Fourier series of a function always converges uniformly to .

Fourier partial sums are continuous functions.

Two different continuous functions might share the same Fourier coefficients.

If is finite, every pointwise convergent sequence is also uniformly convergent.

Pointwise convergence guarantees the limit function is continuous.

If converges uniformly to on and each is continuous, then is continuous.

There exists a sequence of continuous functions that converges pointwise to a discontinuous limit.

If converges pointwise to , then always holds.

Uniform convergence preserves continuity of the limit function.